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Angular Momentum Induced In The Fermionic Vacuum On A
Rotationally-Symmetric Noncompact Riemann Surface: The influence of spatial geometry on the vacuum polarization in
2+1-dimensional spinor electrodynamics is investigated. The vacuum angular
momentum induced by an external static magnetic field is found to depend on
global geometric surface characteristics connected with curvature. The
relevance of the results obtained for the fermion number fractionization is
discussed.
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hep-th
|
Bifurcation and pattern changing with two real scalar fields: This work deals with bifurcation and pattern changing in models described by
two real scalar fields. We consider generic models with quartic potentials and
show that the number of independent polynomial coefficients affecting the
ratios between the various domain wall tensions can be reduced to 4 if the
model has a superpotential. We then study specific one-parameter families of
models and compute the wall tensions associated with both BPS and non-BPS
sectors. We show how bifurcation can be associated to modification of the
patterns of domain wall networks and illustrate this with some examples which
may be relevant to describe realistic situations of current interest in high
energy physics. In particular, we discuss a simple solution to the cosmological
domain wall problem.
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hep-th
|
Moduli Spaces for D-branes at the Tip of a Cone: For physicists: We show that the quiver gauge theory derived from a
Calabi-Yau cone via an exceptional collection of line bundles on the base has
the original cone as a component of its classical moduli space. For
mathematicians: We use data from the derived category of sheaves on a Fano
surface to construct a quiver, and show that its moduli space of
representations has a component which is isomorphic to the anticanonical cone
over the surface.
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hep-th
|
Supersymmetric Intersecting Branes in Time-dependent Backgrounds: We construct a family of supersymmetric solutions in time-dependent
backgrounds in supergravity theories. One class of the solutions are
intersecting brane solutions and another class are brane solutions in pp-wave
backgrounds, and their intersection rules are also given. The relation to
existing literature is also discussed. An example of D1-D5 with linear null
dilaton together with its possible dual theory is briefly discussed.
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hep-th
|
Vulcanized Vortex: We investigate vortex configurations with the "vulcanization" term inspired
by the renormalization of $\phi_\star^4$ theory in the canonical
$\theta$-deformed noncommutativity. We focus on the classical limit of the
theory described by a single parameter which is the ratio of the vulcanization
and the noncommutativity parameters. We perform numerical calculations and find
that nontopological vortex solutions exist as well as Q-ball type solutions,
but topological vortex solutions are not admitted.
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hep-th
|
Bootstrapping the String KLT Kernel: We show that a generalized version of the 4-point string theory KLT
double-copy map is the most general solution to the minimal-rank double-copy
bootstrap in effective field theory. This follows from significant restrictions
of the 4-point map resulting from the 6-point bootstrap analysis. The
generalized 4-point double-copy map is defined by a function with only two
parameters times a simple function that is symmetric in $s,t,u$. The two
parameters can be interpreted as independent choices of $\alpha'$, one for each
of the two sets of amplitudes double-copied with the map. Specifically, each of
those two sets of amplitudes must obey either the string monodromy relations or
the field theory KK & BCJ relations; there are no other options. We propose a
closed form of the new double-copy map that interpolates between the original
KLT string double-copy and the open & closed string period integrals. The
construction clarifies the "single-valued projection" property of the Riemann
zeta-function values for the 4-point string theory double copy.
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hep-th
|
Generating Vector Boson Masses: If the Higgs particle is never found, one will need an alternative theory for
vector boson masses. I propose such a theory involving an antisymmetric tensor
potential coupled to a gauge field.
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hep-th
|
T-duality and U-duality in toroidally-compactified strings: We address the issue of T-duality and U-duality symmetries in the
toroidally-compactified type IIA string. It is customary to take as a starting
point the dimensionally-reduced maximal supergravity theories, with certain
field strengths dualised such that the classical theory exhibits a global
$E_{n(n)}$ symmetry, where n=11-D in D dimensions. A discrete subgroup then
becomes the conjectured U-duality group. In dimensions D\le 6, these necessary
dualisations include NS-NS fields, whose potentials, rather than merely their
field strengths, appear explicitly in the couplings to the string worldsheet.
Thus the usually-stated U-duality symmetries act non-locally on the fundamental
fields of perturbative string theory. At least at the perturbative level, it
seems to be more appropriate to consider the symmetries of the versions of the
lower-dimensional supergravities in which no dualisations of NS-NS fields are
required, although dualisations of the R-R fields are permissible since these
couple to the string through their field strengths. Taking this viewpoint, the
usual T-duality groups survive unscathed, as one would hope since T-duality is
a perturbative symmetry, but the U-duality groups are modified in D\le 6.
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hep-th
|
A Note on a Generalized AHM Model with Analytical Vortex Solutions: We study topological vortex solutions in a generalized Abelian Higgs model
with non-polynomial dielectric and potential functions. These quantities are
chosen by requiring integrability of the self-dual limit of the theory for all
values of the magnetic flux. All the vortex profiles are described by exact
analytical expressions that solve the self-dual vortex equations. There is only
a symmetry-breaking superconducting phase and the model sustains regular
phenomenology.
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hep-th
|
Generalized heat kernel coefficients: Following Osipov and Hiller, a generalized heat kernel expansion is
considered for the effective action of bosonic operators. In this
generalization, the standard heat kernel expansion, which counts inverse powers
of a c-number mass parameter, is extended by allowing the mass to be a matrix
in flavor space. We show that the generalized heat kernel coefficients can be
related to the standard ones in a simple way. This holds with or without trace
and integration over spacetime, to all orders and for general flavor spaces.
Gauge invariance is manifest.
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hep-th
|
Entanglement of Purification and Projective Measurement in CFT: We investigate entanglement of purification in conformal field theory. By
using Reeh-Schlieder theorem, we construct a set of the purification states for
$\rho_{AB}$, where $\rho_{AB}$ is reduced density matrix for subregion $AB$ of
a global state $\rho$. The set can be approximated by acting all the unitary
observables,located in the complement of subregion $AB$, on the global state
$\rho$, as long as the global state $\rho$ is \text{cyclic} for every local
algebra, e.g., the vacuum state. Combining with the gravity explanation of
unitary operations in the context of the so-called surface/state
correspondence, we prove the holographic EoP formula. We also explore the
projective measurement with the conformal basis in conformal field theory and
its relation to the minimization procedure of EoP. Interestingly, though the
projective measurement is not a unitary operator, the difference in some limits
between holographic EoP and the entanglement entropy after a suitable
projective measurement is a constant $\frac{c}{3}\log 2$ up to some
contributions from boundary. This suggests the states after projective
measurements may approximately be taken as the purification state corresponding
to the minimal value of the procedure.
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hep-th
|
Smooth non-extremal D1-D5-P solutions as charged gravitational
instantons: We present an alternative and more direct construction of the
non-supersymmetric D1-D5-P supergravity solutions found by Jejjala, Madden,
Ross and Titchener. We show that these solutions --- with all three charges and
both rotations turned on --- can be viewed as a charged version of the
Myers-Perry instanton. We present an inverse scattering construction of the
Myers-Perry instanton metric in Euclidean five-dimensional gravity. The angular
momentum bounds in this construction turn out to be precisely the ones
necessary for the smooth microstate geometries. We add charges on the
Myers-Perry instanton using appropriate SO(4,4) hidden symmetry
transformations. The full construction can be viewed as an extension and
simplification of a previous work by Katsimpouri, Kleinschmidt and Virmani.
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hep-th
|
Ambiguity in mana and magic definition and knot states: We study the Mana and Magic for quantum states. They have a standard
definition through the Clifford group, which is finite and thus classically
computable. We introduce a modified Mana and Magic, which keep their main
property of classical computability, while making other states classically
computable. We also apply these new definitions to the studies of knot states
of 2-strand knots.
|
hep-th
|
Quantum corrected gravitational potential beyond monopole-monopole
interactions: We investigate spin- and velocity-dependent contributions to the
gravitational inter-particle potential. The methodology adopted here is based
on the expansion of the effective action in terms of form factors encoding
quantum corrections. Restricting ourselves to corrections up to the level of
the graviton propagator, we compute, in terms of general form factors, the
non-relativistic gravitational potential associated with the scattering of
spin-0 and -1/2 particles. We discuss comparative aspects concerning different
types of scattered particles and we also establish some comparisons with the
case of electromagnetic potentials. Moreover, we apply our results to explicit
examples of form factors based on non-perturbative approaches for quantum
gravity. Finally, the cancellation of Newtonian singularity is analysed in the
presence of terms beyond the monopole-monopole sector.
|
hep-th
|
Affine Symmetries for ABJM Partition Function and its Generalization: Partially motivated by the fact that the grand partition function of the ABJM
theory or its generalization is expressed by a spectral operator enjoying
symmetries of the Weyl group, it was found that the grand partition function
satisfies the q-Painleve equation, which is constructed from the affine Weyl
group. In this paper we clarify the affine symmetries of the grand partition
function. With the affine symmetries, we find that the grand partition function
extends naturally outside the fundamental domain of duality cascades and once
the Painleve equation holds in the fundamental domain, so does it outside.
|
hep-th
|
Self--dual Lorentzian wormholes in n--dimensional Einstein gravity: A family of spherically symmetric, static and self--dual Lorentzian wormholes
is obtained in n--dimensional Einstein gravity. This class of solutions
includes the n--dimensional versions of the Schwarzschild black hole and the
spatial--Schwarzschild traversable wormhole. Using isotropic coordinates we
study the geometrical structure of the solution, and delineate the domains of
the free parameters for which wormhole, naked singular geometries and the
Schwarzschild black hole are obtained. It is shown that, in the lower
dimensional Einstein gravity without cosmological constant, we can not have
self--dual Lorentzian wormholes.
|
hep-th
|
The Canonical Symmetry and Hamiltonian Formalism. I. Conservation Laws: The properties of the canonical symmetry of the nonlinear Schr\"odinger
equation are investigated. The densities of the local conservation laws for
this system are shown to change under the action of the canonical symmetry by
total space derivatives.
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hep-th
|
A Web of 2d Dualities: ${\bf Z}_2$ Gauge Fields and Arf Invariants: We describe a web of well-known dualities connecting quantum field theories
in $d=1+1$ dimensions. The web is constructed by gauging ${\bf Z}_2$ global
symmetries and includes a number of perennial favourites such as the
Jordan-Wigner transformation, Kramers-Wannier duality, bosonization of a Dirac
fermion, and T-duality. There are also less-loved examples, such as non-modular
invariant $c=1$ CFTs that depend on a background spin structure.
|
hep-th
|
Quantization Rules for Dynamical Systems: We discuss a manifestly covariant way of arriving at the quantization rules
based on causality, with no reference to Poisson or Peierls brackets of any
kind.
|
hep-th
|
The three-loop Adler $D$-function for ${\cal N}=1$ SQCD with various
renormalization prescriptions: The three-loop Adler $D$-function for ${\cal N}=1$ SQCD in the
$\overline{\mbox{DR}}$ scheme is calculated. It appears that the result does
not satisfy NSVZ-like equation which relates the $D$-function to the anomalous
dimension of the matter superfields. However this NSVZ-like equation can be
restored by a special tuning of the renormalization scheme. Also we demonstrate
that the $D$-function defined in terms of the bare coupling does not satisfy
the NSVZ-like equation in the case of using the regularization by dimensional
reduction. The scheme-dependence of the $D$-function written in the form of the
$\beta$-expansion is briefly discussed.
|
hep-th
|
Breakdown of Cluster Decomposition in Instanton Calculations of the
Gluino Condensate: A longstanding puzzle concerns the calculation of the gluino condensate
<{tr\lambda^2\over 16\pi^2}> = c\Lambda^3 in N=1 supersymmetric SU(N) gauge
theory: so-called weak-coupling instanton (WCI) calculations give c=1, whereas
strong-coupling instanton (SCI) calculations give, instead,
c=2[(N-1)!(3N-1)]^{-1/N}. By examining correlators of this condensate in
arbitrary multi-instanton sectors, we cast serious doubt on the SCI calculation
of <{tr\lambda^2\over 16\pi^2}> by showing that an essential step --- namely
cluster decomposition --- is invalid. We also show that the addition of a
so-called Kovner-Shifman vacuum (in which <{tr\lambda^2\over 16\pi^2}> = 0)
cannot straightforwardly resolve this mismatch.
|
hep-th
|
Causality and classical dispersion relations: We explore the consequences of relativistic causality and covariant stability
for short-wavelength dispersion relations in classical systems. For excitations
described by a finite number of partial differential equations, as is the case
in relativistic hydrodynamics, we give causality and covariant stability
constraints on the excitation's frequency at large momenta.
|
hep-th
|
Israel--Wilson--Perjés Solutions in Heterotic String Theory: We present a simple algorithm to obtain solutions that generalize the
Israel--Wilson--Perj\'es class for the low-energy limit of heterotic string
theory toroidally compactified from D=d+3 to three dimensions. A remarkable map
existing between the Einstein--Maxwell (EM) theory and the theory under
consideration allows us to solve directly the equations of motion making use of
the matrix Ernst potentials connected with the coset matrix of heterotic string
theory. For the particular case d=1 (if we put n=6, the resulting theory can be
considered as the bosonic part of the action of D=4, N=4 supergravity) we
obtain explicitly a dyonic solution in terms of one real 2\times 2--matrix
harmonic function and 2n real constants (n being the number of Abelian vector
fields). By studying the asymptotic behaviour of the field configurations we
define the charges of the system. They satisfy the
Bogomol'nyi--Prasad--Sommmerfeld (BPS) bound.
|
hep-th
|
Correlators of Vertex Operators for Circular Strings with Winding
Numbers in AdS5xS5: We compute semiclassically the two-point correlator of the marginal vertex
operators describing the rigid circular spinning string state with one large
spin and one windining number in AdS_5 and three large spins and three winding
numbers in S^5. The marginality condition and the conformal invariant
expression for the two-point correlator obtained by using an appropriate vertex
operator are shown to be associated with the diagonal and off-diagonal Virasoro
constraints respectively. We evaluate semiclassically the three-point
correlator of two heavy circular string vertex operators and one zero-momentum
dilaton vertex operator and discuss its relation with the derivative of the
dimension of the heavy circular string state with respect to the string
tension.
|
hep-th
|
Canonical invariance of spatially covariant scalar-tensor theory: We investigate invariant canonical transformations of a spatially covariant
scalar-tensor theory of gravity, called the XG theory, by which the action or
the Hamiltonian and the primary constraints keep their forms invariant. We
derive the Hamiltonian in a non perturbative manner and complete the
Hamiltonian analysis for all regions of the theory. We confirm that the theory
has at most 3 degrees of freedom in all regions of the theory as long as the
theory has the symmetry under the spatial diffeormorphism. Then, we derive the
invariant canonical transformation by using the infinitesimal transformation.
The invariant metric transformation of the XG theory contains a vector product
as well as the disformal transformation. The vector product and the disformal
factor can depend on the higher order derivative terms of the scalar field and
the metric. In addition, we discover the invariant canonical transformation
which transforms the momentum of the metric. Using the invariant
transformation, we study the relation between the Horndeski theory and the GLPV
theory, and find that we can not obtain the arbitrary GLPV theory from the
Horndeski theory through the invariant canonical transformation we have found.
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hep-th
|
$T\bar{T}$ deformed partition functions: We demonstrate the presence of modular properties in partition functions of
$T\bar{T}$ deformed conformal field theories. These properties are verified
explicitly for the deformed free boson. The modular features facilitate a
derivation of the asymptotic density of states in these theories, which turns
out to interpolate between Cardy and Hagedorn behaviours. We also point out a
sub-sector of the spectrum that remains undeformed under the $T\bar{T}$ flow.
Finally, we comment on the deformation of the CFT vacuum character and its
implications for the holographic dual.
|
hep-th
|
Statistical mechanics for dilatations in N=4 super Yang--Mills theory: Matrix model describing the anomalous dimensions of composite operators in
$\mathcal{N}=4$ super Yang--Mills theory up to one-loop level is considered at
finite temperature. We compute the thermal effective action for this model,
which we define as the log of the partition function restricted to the states
of given fixed length and spin. The result is obtained in the limits of high
and low temperature.
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hep-th
|
A Comment on the Odd Flows for the Supersymmetric KdV equation: In a recent paper Dargis and Mathieu introduced integrodifferential odd flows
for the supersymmetric KdV equation. These flows are obtained from the nonlocal
conservation laws associated with the fourth root of its Lax operator. In this
note I show that only half of these flows are of the standard Lax form, while
the remaining half provide us with hamiltonians for an SKdV-type reduction of a
new supersymmetric hierarchy. This new hierarchy is shown to be closely related
to the Jacobian supersymmetric KP-hierarchy of Mulase and Rabin. A detailed
study of the algebra of additional symmetries of this new hierarchy reveals
that it is isomorphic to the super-W_{1+\infty} algebra, thus making it a
candidate for a possible interrelationship between superintegrability and
two-dimensional supergravity.
|
hep-th
|
BRST invariant $CP^{1}$ model through improved Dirac quantization: The Batalin-Fradkin-Tyutin (BFT) scheme, which is an improved version of
Dirac quantization, is applied to the $CP^1$ model, and the compact form of a
nontrivial first-class Hamiltonian is directly obtained by introducing the BFT
physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through
the standard path-integral procedure. Furthermore, performing collective
coordinate quantization we obtain energy spectrum of rigid rotator in the
$CP^1$ model. Exploiting the Hopf bundle, we also show that the $CP^1$ model is
exactly equivalent to the O(3) nonlinear sigma model at the canonical level.
|
hep-th
|
Fluctuation and Dissipation from a Deformed String/Gauge Duality Model: Using a Lorentz invariant deformed string/gauge duality model at finite
temperature we calculate the thermal fluctuation and the corresponding linear
response, verifying the fluctuation-dissipation theorem. The deformed AdS$_5$
is constructed by the insertion of an exponential factor $\exp(k/r^2)$ in the
metric. We also compute the string energy and the mean square displacement in
order to investigate the ballistic and diffusive regimes. Furthermore we have
studied the dissipation and the linear response in the zero temperature
scenario.
|
hep-th
|
Supergravity couplings: a geometric formulation: This report provides a pedagogical introduction to the description of the
general Poincare supergravity/matter/Yang-Mills couplings using methods of
Kahler superspace geometry. At a more advanced level this approach is
generalized to include tensor field and Chern-Simons couplings in supersymmetry
and supergravity, relevant in the context of weakly and strongly coupled string
theories.
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hep-th
|
Discrete Theta Angles, Symmetries and Anomalies: Gauge theories in various dimensions often admit discrete theta angles, that
arise from gauging a global symmetry with an additional symmetry protected
topological (SPT) phase. We discuss how the global symmetry and 't Hooft
anomaly depends on the discrete theta angles by coupling the gauge theory to a
topological quantum field theory (TQFT). We observe that gauging an Abelian
subgroup symmetry, that participates in symmetry extension, with an additional
SPT phase leads to a new theory with an emergent Abelian symmetry that also
participates in a symmetry extension. The symmetry extension of the gauge
theory is controlled by the discrete theta angle which comes from the SPT
phase. We find that discrete theta angles can lead to two-group symmetry in 4d
QCD with $SU(N),SU(N)/\mathbb{Z}_k$ or $SO(N)$ gauge groups as well as various
3d and 2d gauge theories.
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hep-th
|
Proof of a three-loop relation between the Regge limits of four-point
amplitudes in N=4 SYM and N=8 supergravity: A previously proposed all-loop-orders relation between the Regge limits of
four-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8
supergravity is established at the three-loop level. We show that the Regge
limit of known expressions for the amplitudes obtained using generalized
unitarity simplifies in both cases to a (modified) sum over three-loop ladder
and crossed-ladder scalar diagrams. This in turn is consistent with the result
obtained using the eikonal representation of the four-point gravity amplitude.
A possible exact three-loop relation between four-point amplitudes is also
considered.
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hep-th
|
On Lie point symmetry of classical Wess-Zumino-Witten model: We perform the group analysis of Witten's equations of motion for a particle
moving in the presence of a magnetic monopole, and also when constrained to
move on the surface of a sphere, which is the classical Wess-Zumino-Witten
model. We also consider variations of this model. Our analysis gives the
generators of the corresponding Lie point symmetries. The Lie symmetry
corresponding to Kepler's third law is obtained in two related examples.
|
hep-th
|
Complementarity in Wormhole Chromodynamics: The electric charge of a wormhole mouth and the magnetic flux ``linked'' by
the wormhole are non-commuting observables, and so cannot be simultaneously
diagonalized. We use this observation to resolve some puzzles in wormhole
electrodynamics and chromodynamics. Specifically, we analyze the color electric
field that results when a colored object traverses a wormhole, and we discuss
the measurement of the wormhole charge and flux using Aharonov-Bohm
interference effects. We suggest that wormhole mouths may obey conventional
quantum statistics, contrary to a recent proposal by Strominger.
|
hep-th
|
Extremal Black Brane Attractors on The Elliptic Curve: Reconsidering the analysis of the moduli space of N=2 eight dimensional
supergravity coupled to seven scalars, we propose a new scalar manifold
factorization given by \frac{\textsc {SO(2,2)}}{{\textsc{SO(2)}}\times
{\textsc{SO(2)}}}\times \frac{\textsc{SO(2,1)}}{\textsc{SO(2)}}\times \textsc
{SO(1,1)}. This factorization is supported by the appearance of three solutions
of Type IIA extremal black p-branes (p=0,1,2) with AdS_{p+2}\times S^{6-p}
near-horizon geometries in eight dimensions. We analyze the corresponding
attractor mechanism. In particular, we give an interplay between the scalar
manifold factors and the extremal black p-brane charges. Then we show that the
dilaton can be stabilized by the dyonic black 2-brane charges.
|
hep-th
|
On the renormalisation group for the boundary Truncated Conformal Space
Approach: In this paper we continue the study of the truncated conformal space approach
to perturbed boundary conformal field theories. This approach to perturbation
theory suffers from a renormalisation of the coupling constant and a
multiplicative renormalisation of the Hamiltonian. We show how these two
effects can be predicted by both physical and mathematical arguments and prove
that they are correct to leading order for all states in the TCSA system. We
check these results using the TCSA applied to the tri-critical Ising model and
the Yang-Lee model. We also study the TCSA of an irrelevant
(non-renormalisable) perturbation and find that, while the convergence of the
coupling constant and energy scales are problematic, the renormalised and
rescaled spectrum remain a very good fit to the exact result, and we find a
numerical relationship between the IR and UV couplings describing a particular
flow. Finally we study the large coupling behaviour of TCSA and show that it
accurately encompasses several different fixed points.
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hep-th
|
Comments on Quivers and Fractons: We discuss certain structural analogies between supersymmetric quiver gauge
theories and lattice models leading to fracton phases of matter. In particular,
classes of quiver models can be viewed as lattice models having sub-system
symmetries, dimensions of moduli spaces growing linearly with the size of the
lattice, and having excitations with limited mobility (with "excitations" and
"mobility" properly defined).
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hep-th
|
Basic zeta functions and some applications in physics: It is the aim of these lectures to introduce some basic zeta functions and
their uses in the areas of the Casimir effect and Bose-Einstein condensation. A
brief introduction into these areas is given in the respective sections. We
will consider exclusively spectral zeta functions, that is zeta functions
arising from the eigenvalue spectrum of suitable differential operators. There
is a set of technical tools that are at the very heart of understanding
analytical properties of essentially every spectral zeta function. Those tools
are introduced using the well-studied examples of the Hurwitz, Epstein and
Barnes zeta function. It is explained how these different examples of zeta
functions can all be thought of as being generated by the same mechanism,
namely they all result from eigenvalues of suitable (partial) differential
operators. It is this relation with partial differential operators that
provides the motivation for analyzing the zeta functions considered in these
lectures. Motivations come for example from the questions "Can one hear the
shape of a drum?" and "What does the Casimir effect know about a boundary?".
Finally "What does a Bose gas know about its container?"
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hep-th
|
A Relativistic Quaternionic Wave Equation: We study a one-component quaternionic wave equation which is relativistically
covariant. Bi-linear forms include a conserved 4-current and an antisymmetric
second rank tensor. Waves propagate within the light-cone and there is a
conserved quantity which looks like helicity. The principle of superposition is
retained in a slightly altered manner. External potentials can be introduced in
a way that allows for gauge invariance. There are some results for scattering
theory and for two-particle wavefunctions as well as the beginnings of second
quantization. However, we are unable to find a suitable Lagrangian or an
energy-momentum tensor.
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hep-th
|
Exact One-Point Function of N=1 super-Liouville Theory with Boundary: In this paper, exact one-point functions of N=1 super-Liouville field theory
in two-dimensional space-time with appropriate boundary conditions are
presented. Exact results are derived both for the theory defined on a
pseudosphere with discrete (NS) boundary conditions and for the theory with
explicit boundary actions which preserves super conformal symmetries. We
provide various consistency checks. We also show that these one-point functions
can be related to a generalized Cardy conditions along with corresponding
modular $S$-matrices. Using this result, we conjecture the dependence of the
boundary two-point functions of the (NS) boundary operators on the boundary
parameter.
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hep-th
|
Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities: The chiral superstring measure constructed in the earlier papers of this
series for general gravitino slices is examined in detail for slices supported
at two points x_\alpha. In this case, the invariance of the measure under
infinitesimal changes of gravitino slices established previously is
strengthened to its most powerful form: the measure is shown, point by point on
moduli space, to be locally and globally independent from the points x_\alpha,
as well as from the superghost insertion points p_a, q_\alpha introduced
earlier as computational devices. In particular, the measure is completely
unambiguous. The limit x_\alpha = q_\alpha is then well defined. It is of
special interest, since it elucidates some subtle issues in the construction of
the picture-changing operator Y(z) central to the BRST formalism. The formula
for the chiral superstring measure in this limit is derived explicitly.
|
hep-th
|
Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras: We study realizations of the exceptional non-linear (quadratically generated,
or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine
symmetry currents, respectively. Both the N=8 and N=7 algebras admit unitary
highest-weight representations in terms of a single boson and free fermions in
8 of Spin(7) and 7 of G_2, with the central charges c_8=26/5 and c_7=5,
respectively. Furthermore, we show that the general coset Ans"atze for the N=8
and N=7 algebras naturally lead to the coset spaces SO(8)xU(1)/SO(7) and
SO(7)xU(1)/G_2, respectively, as the additional consistent solutions for
certain values of the central charge. The coset space SO(8)/SO(7) is the
seven-sphere S^7, whereas the space SO(7)/G_2 represents the seven-sphere with
torsion, S^7_T. The division algebra of octonions and the associated triality
properties of SO(8) play an essential role in all these realizations. We also
comment on some possible applications of our results to string theory.
|
hep-th
|
The Search for Zoo-Perparticles: This paper reviews the covariant formalism of N=1, D=10 classical
superparticle models. It discusses the local invariances of a number of
superparticle actions and highlights the problem of finding a covariant
quantization scenario. Covariant quantization has proved problematic, but it
has motivated in seeking alternative approaches that avoids those found in
earlier models. It also shows new covariant superparticle theories formulated
in extended spaces that preserve certain canonical form in phase-space, and
easy to quantize by using the Batalin-Vilkovisky procedure, as the gauge
algebra of their constraints only closes on-shell. The mechanics actions
describe particles moving in a superspace consisting of the usual $N=1$
superspace, together with an extra spinor or vector coordinate. A light-cone
analysis shows that all these new superparticle models reproduce the physical
spectrum of the N=1 super-Yang-Mills theory.
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hep-th
|
Exact Inner Metric and Microscopic State of AdS$_3$-Schwarzschld BHs: Through full solvability of 2+1 dimensional general relativity we derive out
exact dynamic inner metric of collapsing stars with inhomogeneous initial mass
distribution but joining with outside Anti-deSitt-Schwarzschild black holes
smoothly. We prove analytically by standard quantum mechanics that the
log-number of such solutions, or microscopic states of the system is
proportional to the perimeter of the outside black holes. Key formulas for
generalizing to 3+1D Schwarzschild black holes are also presented. Our result
provides a bulk space viewpoint to questions on what the microscopic degrees of
freedom are and who their carriers are in various holographic and/or asymptotic
symmetry methods to black hole entropies. It may also shed light for
singularity theorem and cosmic censorship related researches.
|
hep-th
|
Torsional Regularization of Self-Energy and Bare Mass of Electron: In the presence of spacetime torsion, the momentum components do not commute;
therefore, in quantum field theory, summation over the momentum eigenvalues
will replace integration over the momentum. In the Einstein--Cartan theory of
gravity, in which torsion is coupled to spin, the separation between the
eigenvalues increases with the magnitude of the momentum. Consequently, this
replacement regularizes divergent integrals in Feynman diagrams with loops by
turning them into convergent sums. In this article, we apply torsional
regularization to the self-energy of a charged lepton in quantum
electrodynamics. We show that this procedure eliminates the ultraviolet
divergence. We also show that torsion gives a photon a small nonzero mass,
which regularizes the infrared divergence. In the end, we calculate the finite
bare masses of the electron, muon, and tau lepton: $0.4329\,\mbox{MeV}$,
$90.95\,\mbox{MeV}$, and $1543\,\mbox{MeV}$, respectively. These values
constitute about $85\%$ of the observed, re-normalized masses.
|
hep-th
|
Astrophysical Violations of the Kerr Bound as a Possible Signature of
String Theory: In 4D general relativity, the angular momentum of a black hole is limited by
the Kerr bound. We suggest that in string theory, this bound can be breached
and compact black-hole-like objects can spin faster. Near such "superspinars,"
the efficiency of energy transfer from the accreting matter to radiation can
reach 100%, compared to the maximum efficiency of 42% of the extremal Kerr (or
6% of the Schwarzschild) black hole. Finding such superspinning objects as
active galactic nuclei, GBHCs, or sources of gamma ray bursts, could be viewed
as experimental support for string theory.
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hep-th
|
Chaos around Holographic Regge Trajectories: Using methods of Hamiltonian dynamical systems, we show analytically that a
dynamical system connected to the classical spinning string solution
holographically dual to the principal Regge trajectory is non-integrable. The
Regge trajectories themselves form an integrable island in the total phase
space of the dynamical system. Our argument applies to any gravity background
dual to confining field theories and we verify it explicitly in various
supergravity backgrounds: Klebanov-Strassler, Maldacena-Nunez, Witten QCD and
the AdS soliton. Having established non-integrability for this general class of
supergravity backgrounds, we show explicitly by direct computation of the
Poincare sections and the largest Lyapunov exponent, that such strings have
chaotic motion.
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hep-th
|
Hierarchy problem and the cosmological constant in a five-dimensional
Brans-Dicke brane world model: We discuss a new solution, admitting the existence of dS_{4} branes, in
five-dimensional Brans-Dicke theory. It is shown that, due to a special form of
a bulk scalar field potential, for certain values of the model parameters the
effective cosmological constant can be made small on the brane, where the
hierarchy problem of gravitational interaction is solved. We also discuss new
stabilization mechanism which is based on the use of auxiliary fields.
|
hep-th
|
Hawking temperature from tunnelling formalism: It has recently been suggested that the attempt to understand Hawking
radiation as tunnelling across black hole horizons produces a Hawking
temperature double the standard value. It is explained here how one can obtain
the standard value in the same tunnelling approach.
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hep-th
|
2d Index and Surface operators: In this paper we compute the superconformal index of 2d (2,2) supersymmetric
gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is
computed by a unitary matrix integral much like the matrix integral that
computes 4d superconformal index. We compute the 2d index explicitly for a
number of examples. In the case of abelian gauge theories we see that the index
is invariant under flop transition and CY-LG correspondence. The index also
provides a powerful check of the Seiberg-type duality for non-abelian gauge
theories discovered by Hori and Tong.
In the later half of the paper, we study half-BPS surface operators in N=2
superconformal gauge theories. They are engineered by coupling the 2d (2,2)
supersymmetric gauge theory living on the support of the surface operator to
the 4d N=2 theory, so that different realizations of the same surface operator
with a given Levi type are related by a 2d analogue of the Seiberg duality. The
index of this coupled system is computed by using the tools developed in the
first half of the paper. The superconformal index in the presence of surface
defect is expected to be invariant under generalized S-duality. We demonstrate
that it is indeed the case. In doing so the Seiberg-type duality of the 2d
theory plays an important role.
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hep-th
|
New Multicritical Random Matrix Ensembles: In this paper we construct a class of random matrix ensembles labelled by a
real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves
like $|x|^\alpha$. The eigenvalue spacing near zero scales like
$1/N^{1/(1+\alpha)}$ and thus these ensembles are representatives of a {\em
continous} series of new universality classes. We study these ensembles both in
the bulk and on the scale of eigenvalue spacing. In the former case we obtain
formulas for the eigenvalue density, while in the latter case we obtain
approximate expressions for the scaling functions in the microscopic limit
using a very simple approximate method based on the location of zeroes of
orthogonal polynomials.
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hep-th
|
Stability of $AdS_p x S^n x S^{q-n}$ Compactifications: We examine the stability of ${\rm AdS}_p \times {\rm S}^n \times {\rm
S}^{q-n}$. The initial data constructed by De Wolfe et al \cite{Gary} has been
carefully analyised and we have confirmed that there is no lower bound for the
total mass for $q< 9$. The effective action on ${\rm AdS}_p$ has been derived
for dilatonic compactification of the system to describe the non-linear
fluctuation of the background space-time. The stability is discussed applying
the positive energy theorem to the effective theory on AdS, which again shows
the stability for $q \geq 9$.
|
hep-th
|
Integrable XYZ Model with Staggered Anisotropy Parameter: We apply to the XYZ model the technique of construction of integrable models
with staggered parameters, presented recently for the XXZ case. The solution of
modified Yang-Baxter equations is found and the corresponding integrable
zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ
case in the appropriate limit.
|
hep-th
|
Local Fluid Dynamical Entropy from Gravity: Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4
super Yang Mills theory have recently been constructed perturbatively in the
long wavelength limit. We demonstrate that these geometries all have regular
event horizons, and determine the location of the horizon order by order in a
boundary derivative expansion. Intriguingly, the derivative expansion allows us
to determine the location of the event horizon in the bulk as a local function
of the fluid dynamical variables. We define a natural map from the boundary to
the horizon using ingoing null geodesics. The area-form on spatial sections of
the horizon can then be pulled back to the boundary to define a local entropy
current for the dual field theory in the hydrodynamic limit. The area theorem
of general relativity guarantees the positivity of the divergence of the
entropy current thus constructed.
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hep-th
|
Basic hypergeometry of supersymmetric dualities: We introduce several new identities combining basic hypergeometric sums and
integrals. Such identities appear in the context of superconformal index
computations for three-dimensional supersymmetric dual theories. We give both
analytic proofs and physical interpretations of the presented identities.
|
hep-th
|
Symmetries and supersymmetries of the Dirac operators in curved
spacetimes: It is shown that the main geometrical objects involved in all the symmetries
or supersymmetries of the Dirac operators in curved manifolds of arbitrary
dimensions are the Killing vectors and the Killing-Yano tensors of any ranks.
The general theory of external symmetry transformations associated to the usual
isometries is presented, pointing out that these leave the standard Dirac
equation invariant providing the correct spin parts of the group generators.
Furthermore, one analyzes the new type of symmetries generated by the
covariantly constant Killing-Yano tensors that realize certain square roots of
the metric tensor. Such a Killing-Yano tensor produces simultaneously a
Dirac-type operator and the generator of a one-parameter Lie group connecting
this operator with the standard Dirac one. In this way the Dirac operators are
related among themselves through continuous transformations associated to
specific discrete ones. It is shown that the groups of this continuous symmetry
can be only U(1) or SU(2), as those of the (hyper-)Kahler spaces, but arising
even in cases when the requirements for these special geometries are not
fulfilled. To exemplify, the Euclidean Taub-NUT space with its Dirac-type
operators is presented in much details, pointing out that there is an
infinite-loop superalgebra playing the role of a closed dynamical algebraic
structure. As a final topic, we go to consider the properties of the Dirac-type
operators of the Minkowski spacetime.
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hep-th
|
Topological Gravity as the Early Phase of Our Universe: Motivated by string dualities we propose topological gravity as the early
phase of our universe. The topological nature of this phase naturally leads to
the explanation of many of the puzzles of early universe cosmology. A concrete
realization of this scenario using Witten's four dimensional topological
gravity is considered. This model leads to the power spectrum of CMB
fluctuations which is controlled by the conformal anomaly coefficients $a,c$.
In particular the strength of the fluctuation is controlled by $1/a$ and its
tilt by $c g^2$ where $g$ is the coupling constant of topological gravity. The
positivity of $c$, a consequence of unitarity, leads automatically to an IR
tilt for the power spectrum. In contrast with standard inflationary models,
this scenario predicts $\mathcal{O}(1)$ non-Gaussianities for four- and
higher-point correlators and the absence of tensor modes in the CMB
fluctuations.
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hep-th
|
The AdS Virasoro-Shapiro Amplitude: We present a constructive method to compute the AdS Virasoro-Shapiro
amplitude, order by order in AdS curvature corrections. At kth order the answer
takes the form of a genus zero world-sheet integral involving weight 3k
single-valued multiple polylogarithms. The coefficients in our ansatz are
fixed, order by order, by requiring: crossing symmetry; the correct
supergravity limit; the correct structure of poles, determined by dispersive
sum rules; and the dimensions of the first few Konishi-like operators,
available from integrability. We explicitly construct the first two curvature
corrections. Our final answer then reproduces all localisation results and all
CFT data available from integrability, to this order, and produces a wealth of
new CFT data for planar N=4 SYM at strong coupling.
|
hep-th
|
Enhanced D-Brane Categories from String Field Theory: We construct D-brane categories in B-type topological string theory as
solutions to string field equations of motion. Using the formalism of
superconnections, we show that these solutions form a variant of a construction
of Bondal and Kapranov. This analysis is an elaboration on recent work of
Lazaroiu. We also comment on the relation between string field theory and the
derived category approach of Douglas, and Aspinwall and Lawrence.
Non-holomorphic deformations make a somewhat unexpected appearance in this
construction.
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hep-th
|
Holographic entanglement density for spontaneous symmetry breaking: We investigate the properties of the holographic entanglement entropy of the
systems in which the $U(1)$ or the translational symmetry is broken
\textit{spontaneously}. For this purpose, we define the entanglement density of
the strip-subsystems and examine both the first law of entanglement entropy
(FLEE) and the area theorem. We classify the conditions that FLEE and/or the
area theorem obey and show that such a classification may be useful for
characterizing the systems. We also find universalities from both FLEE and the
area theorem. In the spontaneous symmetry breaking case, FLEE is always obeyed
regardless of the type of symmetry: $U(1)$ or translation. For the
translational symmetry, the area theorem is always violated when the symmetry
is weakly broken, independent of the symmetry breaking patterns (explicit or
spontaneous). We also argue that the $\log$ contribution of the entanglement
entropy from the Goldstone mode may not appear in the strongly coupled systems.
|
hep-th
|
A Description of Schwarzschild Black Holes in terms of Intersecting
M-branes and antibranes: Intersecting M-branes are known to describe multi charged black holes. Using
a configuration of such intersecting branes and antibranes, together with
massless excitations living on them, we give a description of Schwarzschild
black holes following Danielsson, Guijosa, and Kruczenski. We calculate the
entropy of these black holes and find that it agrees, upto a numerical factor,
with the entropy of the corresponding Schwarzschild black holes in supergravity
approximation. We give an empirical interpretation of this factor.
|
hep-th
|
Fermionic Zero Mode and String Creation between D4-Branes at Angles: We study the creation of a fundamental string between D4-branes at angles in
string theory. It is shown that $R(-1)^{F}$ part of the one-loop potential of
open string changes its sign due to the change of fermionic zero-mode vacua
when the branes cross each other. As a result the effective potential is
independent of the angles when supersymmetry is partially unbroken, and leads
to a consistent picture that a fundamental string is created in the process. We
also discuss the s-rule in the configuration. The same result is obtained from
the one-loop potential for the orthogonal D4-branes with non-zero field
strength. The result is also confirmed from the tension obtained by deforming
the Chern-Simons term on one D4-brane, which is induced by another tilted
D4-brane.
|
hep-th
|
Supersymmetric K field theories and defect structures: We construct supersymmetric K field theories (i.e., theories with a
non-standard kinetic term) in 1+1 and 2+1 dimensions such that the bosonic
sector just consists of a nonstandard kinetic term plus a potential. Further,
we study the possibility of topological defect formation in these
supersymmetric models. Finally, we consider more general supersymmetric K field
theories where, again, topological defects exist in some cases.
|
hep-th
|
Renormalized Holographic Subregion Complexity under Relevant
Perturbations: We construct renormalized holographic entanglement entropy (HEE) and
subregion complexity (HSC) in the CV conjecture for asymptotically AdS$_4$ and
AdS$_5$ geometries under relevant perturbations. Using the holographic
renormalization method developed in the gauge/gravity duality, we obtain
counter terms which are invariant under coordinate choices. We explicitly
define different forms of renormalized HEE and HSC, according to conformal
dimensions of relevant operators in the $d=3$ and $d=4$ dual field theories. We
use a general embedding for arbitrary entangling subregions and showed that any
choice of the coordinate system gives the same form of the counter terms, since
they are written in terms of curvature invariants and scalar fields on the
boundaries. We show an explicit example of our general procedure. Intriguingly,
we find that a divergent term of the HSC in the asymptotically AdS$_5$ geometry
under relevant perturbations with operators of conformal dimensions in the
range $0< \Delta < \frac{1}{2}\,\, {\rm and} \,\, \frac{7}{2}< \Delta < 4$
cannot be cancelled out by adding any coordinate invariant counter term. This
implies that the HSCs in these ranges of the conformal dimensions are not
renormalizable covariantly.
|
hep-th
|
Null Infinity as a Weakly Isolated Horizon: Null infinity (Scri) arises as a boundary of the Penrose conformal completion
of an asymptotically flat physical space-time. We first note that Scri is a
weakly isolated horizon (WIH), and then show that its familiar properties can
be derived from the general WIH framework. This seems quite surprising because
physics associated with black hole (and cosmological) WIHs is very different
from that extracted at Scri. We show that these differences can be directly
traced back to the fact that Scri is a WIH in the conformal completion rather
than the physical space-time. In particular, the BMS group at Scri stems from
the symmetry group of WIHs. We also introduce a unified procedure to arrive at
fluxes and charges associated with the BMS symmetries at Scri and those
associated with black hole (and cosmological) horizons. This procedure differs
from those commonly used in the literature and its novel elements seem
interesting in their own right. The fact that is there is a single mathematical
framework underlying black hole (and cosmological) horizons and Scri paves the
way to explore the relation between horizon dynamics in the strong field region
and waveforms at infinity. It should also be useful in the analysis of black
hole evaporation in quantum gravity.
|
hep-th
|
Entropy and Black Holes in the Very Early Universe: Model independent arguments following from the Covariant Entropy Principle
imply that causal diamonds in the very early universe were entirely filled with
a single equilibrated system with finite entropy. A universe where this
condition persists forever has no localized excitations. Our own universe
appears to be headed toward such a state. Within a few hundred times its
current age it will approach a state where our local group of galaxies sit in
empty de Sitter space. Eventually, the local group collapse into a black hole,
which evaporates. Localized excitations in de Sitter space are low entropy
constrained states of the vacuum ensemble. The origin of these constraints must
be in the early universe: the apparent horizon must expand after some initial
period, in a constrained state that is the origin of all localized excitations
in the universe. We argue that in global FRW coordinates, this corresponds to
slow roll inflation that ends in a dilute gas of tiny black holes, with mass
determined by the inflationary scale. We then review arguments that these black
holes can account for the Hot Big Bang, baryogenesis, a distinctive pattern of
CMB fluctuations, and possibly primordial black hole dark matter consisting of
larger black holes that survive until the matter dominated era. The more
complicated question of whether these small black holes can evolve in a way
that is consistent with all observational constraints requires computer
simulations that have not yet been done.
|
hep-th
|
Higher-Derivative Chiral Superfield Actions Coupled to N=1 Supergravity: We construct N=1 supergravity extensions of scalar field theories with
higher-derivative kinetic terms. Special attention is paid to the auxiliary
fields, whose elimination leads not only to corrections to the kinetic terms,
but to new expressions for the potential energy as well. For example, a
potential energy can be generated even in the absence of a superpotential. Our
formalism allows one to write a supergravity extension of any higher-derivative
scalar field theory and, therefore, has applications to both particle physics
and cosmological model building. As an illustration, we couple the
higher-derivative DBI action describing a 3-brane in 6-dimensions to N=1
supergravity. This displays a number of new features-- including the fact that,
in the regime where the higher-derivative kinetic terms become important, the
potential tends to be everywhere negative.
|
hep-th
|
Exact g-function flows from the staircase model: Equations are found for exact g-functions corresponding to integrable bulk
and boundary flows between successive unitary c<1 minimal conformal field
theories in two dimensions, confirming and extending previous perturbative
results. These equations are obtained via an embedding of the flows into a
boundary version of Al. Zamolodchikov's staircase model.
|
hep-th
|
Asymptotic symmetries of QED and Weinberg's soft photon theorem: Various equivalences between so-called soft theorems which constrain
scattering amplitudes and Ward identities related to asymptotic symmetries have
recently been established in gauge theories and gravity. So far these
equivalences have been restricted to the case of massless matter fields, the
reason being that the asymptotic symmetries are defined at null infinity. The
restriction is however unnatural from the perspective of soft theorems which
are insensitive to the masses of the external particles.
In this work we remove the aforementioned restriction in the context of
scalar QED. Inspired by the radiative phase space description of massless
fields at null infinity, we introduce a manifold description of time-like
infinity on which the asymptotic phase space for massive fields can be defined.
The "angle dependent" large gauge transformations are shown to have a well
defined action on this phase space, and the resulting Ward identities are found
to be equivalent to Weinberg's soft photon theorem.
|
hep-th
|
Entanglement and mutual information in two-dimensional nonrelativistic
field theories: We carry out a systematic study of entanglement entropy in nonrelativistic
conformal field theories via holographic techniques. After a discussion of
recent results concerning Galilean conformal field theories, we deduce a novel
expression for the entanglement entropy of (1+1)-dimensional Lifshitz field
theories --- this is done both at zero and finite temperature. Based on these
results, we pose a conjecture for the anomaly coefficient of a Lifshitz field
theory dual to new massive gravity. It is found that the Lifshitz entanglement
entropy at finite temperature displays a striking similarity with that
corresponding to a flat space cosmology in three dimensions. We claim that this
structure is an inherent feature of the entanglement entropy for
nonrelativistic conformal field theories. We finish by exploring the behavior
of the mutual information for such theories.
|
hep-th
|
Domain Wall and de Sitter Solutions of Gauged Supergravity: BPS domain wall solutions of gauged supergravities are found, including those
theories which have non-compact gauge groups. These include models that have
both an unstable de Sitter solution and stable domain wall solutions.
|
hep-th
|
A double integral of dlog forms which is not polylogarithmic: Feynman integrals are central to all calculations in perturbative Quantum
Field Theory. They often give rise to iterated integrals of dlog-forms with
algebraic arguments, which in many cases can be evaluated in terms of multiple
polylogarithms. This has led to certain folklore beliefs in the community
stating that all such integrals evaluate to polylogarithms. Here we discuss a
concrete example of a double iterated integral of two dlog-forms that evaluates
to a period of a cusp form. The motivic versions of these integrals are shown
to be algebraically independent from all multiple polylogarithms evaluated at
algebraic arguments. From a mathematical perspective, we study a mixed elliptic
Hodge structure arising from a simple geometric configuration in
$\mathbb{P}^2$, consisting of a modular plane elliptic curve and a set of lines
which meet it at torsion points, which may provide an interesting worked
example from the point of view of periods, extensions of motives, and
L-functions.
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hep-th
|
Towards a string representation of infrared SU(2) Yang-Mills theory: We employ a heat kernel expansion to derive an effective action that
describes four dimensional SU(2) Yang-Mills theory in the infrared limit. Our
result supports the proposal that at large distances the theory is approximated
by the dynamics of knotted string-like fluxtubes which appear as solitons in
the effective theory.
|
hep-th
|
The classical dynamics of gauge theories in the deep infrared: Gauge and gravitational theories in asymptotically flat settings possess
infinitely many conserved charges associated with large gauge transformations
or diffeomorphisms that are nontrivial at infinity. To what extent do these
charges constrain the scattering in these theories? It has been claimed in the
literature that the constraints are trivial, due to a decoupling of hard and
soft sectors for which the conserved charges constrain only the dynamics in the
soft sector. We show that the argument for this decoupling fails due to the
failure in infinite dimensions of a property of symplectic geometry which holds
in finite dimensions. Specializing to electromagnetism coupled to a massless
charged scalar field in four dimensional Minkowski spacetime, we show
explicitly that the two sectors are always coupled using a perturbative
classical computation of the scattering map. Specifically, while the two
sectors are uncoupled at low orders, they are coupled at quartic order via the
electromagnetic memory effect. This coupling cannot be removed by adjusting the
definitions of the hard and soft sectors (which includes the classical analog
of dressing the hard degrees of freedom). We conclude that the conserved
charges yield nontrivial constraints on the scattering of hard degrees of
freedom. This conclusion should also apply to gravitational scattering and to
black hole formation and evaporation.
In developing the classical scattering theory, we show that generic Lorenz
gauge solutions fail to satisfy the matching condition on the vector potential
at spatial infinity proposed by Strominger to define the field configuration
space, and we suggest a way to remedy this. We also show that when soft degrees
of freedom are present, the order at which nonlinearities first arise in the
scattering map is second order in Lorenz gauge, but can be third order in other
gauges.
|
hep-th
|
Finite temperature fermionic condensate and currents in topologically
nontrivial spaces: We investigate the finite temperature fermionic condensate and the
expectation values of the charge and current densities for a massive fermion
field in a spacetime background with an arbitrary number of toroidally
compactified spatial dimensions in the presence of a non-vanishing chemical
potential. Periodicity conditions along compact dimensions are taken with
arbitrary phases and the presence of a constant gauge field is assumed. The
latter gives rise to Aharonov-Bohm-like effects on the expectation values. They
are periodic functions of magnetic fluxes enclosed by compact dimensions with
the period equal to the flux quantum. The current density has nonzero
components along compact dimensions only. Both low- and high-temperature
asymptotics of the expectation values are studied. In particular, it has been
shown that at high temperatures the current density is exponentially
suppressed. This behavior is in sharp contrast with the corresponding
asymptotic in the case of a scalar field, where the current density linearly
grows with the temperature. The features for the models in odd dimensional
spacetimes are discussed. Applications are given to cylindrical and toroidal
nanotubes described within the framework of effective Dirac theory for the
electronic subsystem.
|
hep-th
|
A non-commuting twist in the partition function: We compute a twisted index for an orbifold theory when the twist generating
group does not commute with the orbifold group. The twisted index requires the
theory to be defined on moduli spaces that are compatible with the twist. This
is carried out for CHL models at special points in the moduli space where they
admit dihedral symmetries. The commutator subgroup of the dihedral groups are
cyclic groups that are used to construct the CHL orbifolds. The residual
reflection symmetry is chosen to act as a `twist' on the partition function.
The reflection symmetries do not commute with the orbifolding group and hence
we refer to this as a non-commuting twist. We count the degeneracy of half-BPS
states using the twisted partition function and find that the contribution
comes mainly from the untwisted sector. We show that the generating function
for these twisted BPS states are related to the Mathieu group M_{24}.
|
hep-th
|
Uses of zeta regularization in QFT with boundary conditions: a
cosmo-topological Casimir effect: Zeta regularization has proven to be a powerful and reliable tool for the
regularization of the vacuum energy density in ideal situations. With the
Hadamard complement, it has been shown to provide finite (and meaningful)
answers too in more involved cases, as when imposing physical boundary
conditions (BCs) in two-- and higher--dimensional surfaces (being able to
mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero
depths). What we have considered is the {\it additional} contribution to the cc
coming from the non-trivial topology of space or from specific boundary
conditions imposed on braneworld models (kind of cosmological Casimir effects).
Assuming someone will be able to prove (some day) that the ground value of the
cc is zero, as many had suspected until very recently, we will then be left
with this incremental value coming from the topology or BCs. We show that this
value can have the correct order of magnitude in a number of quite reasonable
models involving small and large compactified scales and/or brane BCs, and
supergravitons.
|
hep-th
|
Thermoelectric Conductivities at Finite Magnetic Field and the Nernst
Effect: We study the thermoelectric conductivities of a strongly correlated system in
the presence of a magnetic field by the gauge/gravity duality. We consider a
class of Einstein-Maxwell-Dilaton theories with axion fields imposing momentum
relaxation. General analytic formulas for the direct current(DC) conductivities
and the Nernst signal are derived in terms of the black hole horizon data. For
an explicit model study, we analyse in detail the dyonic black hole modified by
momentum relaxation. In this model, for small momentum relaxation, the Nernst
signal shows a bell-shaped dependence on the magnetic field, which is a feature
of the normal phase of cuprates. We compute all alternating current(AC)
electric, thermoelectric, and thermal conductivities by numerical analysis and
confirm that their zero frequency limits precisely reproduce our analytic DC
formulas, which is a non-trivial consistency check of our methods. We discuss
the momentum relaxation effects on the conductivities including cyclotron
resonance poles.
|
hep-th
|
One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity: We present an ansatz for all one-loop amplitudes in pure Einstein gravity for
which the n external gravitons have the same outgoing helicity. These loop
amplitudes, which are rational functions of the momenta, also arise in the
quantization of self-dual gravity in four-dimensional Minkowski space. Our
ansatz agrees with explicit computations via D-dimensional unitarity cuts for n
less than or equal to 6. It also has the expected analytic behavior, for all n,
as a graviton becomes soft, and as two momenta become collinear. The gravity
results are closely related to analogous amplitudes in (self-dual) Yang-Mills
theory.
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hep-th
|
Time Lumps in Nonlocal Stringy Models and Cosmological Applications: We study lump solutions in nonlocal toy models and their cosmological
applications. These models are motivated by a description of D-brane decay
within string field theory framework. In order to find cosmological solutions
we use the simplest local approximation keeping only second derivative terms in
nonlocal dynamics. We study a validity of this approximation in flat background
where time lump solutions can be written explicitly. We work out the validity
of this approximation. We show that our models at large time exhibit the
phantom behaviour similar to the case of the string kink.
|
hep-th
|
N=2 Chiral Supergravity in (10 + 2)-Dimensions As Consistent Background
for Super (2 + 2)-Brane: We present a theory of N=2 chiral supergravity in (10+2)-dimensions. This
formulation is similar to N=1 supergravity presented recently using
null-vectors in 12D. In order to see the consistency of this theory, we perform
a simple dimensional reduction to ten-dimensions, reproducing the type IIB
chiral supergravity. We also show that our supergravity can be consistent
background for super (2+2)-brane theory, satisfying fermionic invariance of the
total action. Such supergravity theory without manifest Lorentz invariance had
been predicted by the recent F-theory in twelve-dimensions.
|
hep-th
|
Wilson loops in large N field theories: We propose a method to calculate the expectation values of an operator
similar to the Wilson loop in the large N limit of field theories. We consider
N=4 3+1 dimensional super-Yang-Mills. The prescription involves calculating the
area of a fundamental string worldsheet in certain supergravity backgrounds. We
also consider the case of coincident M-theory fivebranes where one is lead to
calculating the area of M-theory two-branes. We briefly discuss the computation
for 2+1 dimensional super-Yang-Mills with sixteen supercharges which is
non-conformal. In all these cases we calculate the energy of quark-antiquark
pair.
|
hep-th
|
Generalized Poincare algebras and Lovelock-Cartan gravity theory: We show that the Lagrangian for Lovelock-Cartan gravity theory can be
re-formulated as an action which leads to General Relativity in a certain
limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory
invariant under the generalized Poincar\'{e} algebra $\mathfrak{B}_{2n+1},$
while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant
under a subalgebra of the $\mathfrak{B}_{2n+1}$ algebra. It is also shown that
torsion may occur explicitly in the Lagrangian leading to new torsional
Lagrangians, which are related to the Chern-Pontryagin character for the
$B_{2n+1}$ group.
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hep-th
|
Motivic Amplitudes and Cluster Coordinates: In this paper we study motivic amplitudes--objects which contain all of the
essential mathematical content of scattering amplitudes in planar SYM theory in
a completely canonical way, free from the ambiguities inherent in any attempt
to choose particular functional representatives. We find that the cluster
structure on the kinematic configuration space Conf_n(P^3) underlies the
structure of motivic amplitudes. Specifically, we compute explicitly the
coproduct of the two-loop seven-particle MHV motivic amplitude A_{7,2} and find
that like the previously known six-particle amplitude, it depends only on
certain preferred coordinates known in the mathematics literature as cluster
X-coordinates on Conf_n(P^3). We also find intriguing relations between motivic
amplitudes and the geometry of generalized associahedrons, to which cluster
coordinates have a natural combinatoric connection. For example, the
obstruction to A_{7,2} being expressible in terms of classical polylogarithms
is most naturally represented by certain quadrilateral faces of the appropriate
associahedron. We also find and prove the first known functional equation for
the trilogarithm in which all 40 arguments are cluster X-coordinates of a
single algebra. In this respect it is similar to Abel's 5-term dilogarithm
identity.
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hep-th
|
Electron-positron pairs production in a macroscopic charged core: Classical and semi-classical energy states of relativistic electrons bounded
by a massive and charged core with the charge-mass-radio Q/M and macroscopic
radius R_c are discussed. We show that the energies of semi-classical (bound)
states can be much smaller than the negative electron mass-energy (-mc^2), and
energy-level crossing to negative energy continuum occurs. Electron-positron
pair production takes place by quantum tunneling, if these bound states are not
occupied. Electrons fill into these bound states and positrons go to infinity.
We explicitly calculate the rate of pair-production, and compare it with the
rates of electron-positron production by the Sauter-Euler-Heisenberg-Schwinger
in a constant electric field. In addition, the pair-production rate for the
electro-gravitational balance ratio Q/M = 10^{-19} is much larger than the
pair-production rate due to the Hawking processes.
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hep-th
|
Topological Conformal Algebra in $2d$ Gravity Coupled to Minimal Matter: An infinite number of topological conformal algebras with varying central
charges are explicitly shown to be present in $2d$ gravity (treated both in the
conformal gauge and in the light-cone gauge) coupled to minimal matter. The
central charges of the underlying $N=2$ theory in two different gauge choices
are generically found to be different. The physical states in these theories
are briefly discussed in the light of the $N=2$ superconformal symmetry.
|
hep-th
|
Managing $γ_5$ in Dimensional Regularization II: the Trace with
more $γ_5$: In the present paper we evaluate the anomaly for the abelian axial current in
a non abelian chiral gauge theory, by using dimensional regularization. This
amount to formulate a procedure for managing traces with more than one
$\gamma_5$. \par The suggested procedure obeys Lorentz covariance and
cyclicity, at variance with previous approaches (e.g. the celebrated 't Hooft
and Veltman's where Lorentz is violated) \par The result of the present paper
is a further step forward in the program initiated by a previous work on the
traces involving a single $\gamma_5$. The final goal is an unconstrained
definition of $\gamma_5$ in dimensional regularization. Here, in the evaluation
of the anomaly, we profit of the axial current conservation equation, when
radiative corrections are neglected. This kind of tool is not always exploited
in field theories with $\gamma_5$, e.g. in the use of dimensional
regularization of infrared and collinear divergences.
|
hep-th
|
Absence of the Gribov ambiguity in a quadratic gauge: The Gribov ambiguity exists in various gauges except algebraic gauges.
However, algebraic gauges are not Lorentz invariant, which is their fundamental
flaw. In addition, they are not generally compatible with the boundary
conditions on the gauge fields, which are needed to compactify the space i.e.,
the ambiguity continues to exist on a compact manifold. Here we discuss a
quadratic gauge fixing, which is Lorentz invariant. We consider an example of a
spherically symmetric gauge field configuration in which we prove that this
Lorentz invariant gauge removes the ambiguity on a compact manifold
$\mathbb{S}^3$, when a proper boundary condition on the gauge configuration is
taken into account. Thus, providing one example where the ambiguity is absent
on a compact manifold in the algebraic gauge. We also show that the \tmem{BRST}
invariance is preserved in this gauge.
|
hep-th
|
On the Quantum Origin of Structure in the Inflationary Universe: In this lecture I give a pedagogical introduction to inflationary cosmology
with a special focus on the quantum generation of cosmological perturbations.
|
hep-th
|
Two loop five point integrals: light, heavy and large spin correlators: We evaluated all two loop conformal integrals appearing in five point
correlation functions of protected operators of $\mathcal{N} = 4$ Super
Yang-Mills in several kinematical regimes. Starting from the correlation
function of the lightest operators of the theory, we were able to extract
structure constants of up to two spinning operators for small and large values
of polarizations and spin. We conjectured an universal all loop behaviour for
the large spin small polarization structure constants and comment on the
subtleties of analytically continuing it from finite to large spin. We also
consider correlation functions of heavier operators that get factorized in the
more fundamental object called decagon. We fixed this object at two loops in
general kinematics and studied its physical properties under OPE and null
limits.
|
hep-th
|
Orientifolds, RR Torsion, and K-theory: We analyze the role of RR fluxes in orientifold backgrounds from the point of
view of K-theory, and demonstrate some physical implications of describing
these fluxes in K-theory rather than cohomology. In particular, we show that
certain fractional shifts in RR charge quantization due to discrete RR fluxes
are naturally explained in K-theory. We also show that some orientifold
backgrounds, which are considered distinct in the cohomology classification,
become equivalent in the K-theory description, while others become unphysical.
|
hep-th
|
Towards a Non-Supersymmetric String Phenomenology: Over the past three decades, considerable effort has been devoted to studying
the rich and diverse phenomenologies of heterotic strings exhibiting spacetime
supersymmetry. Unfortunately, during this same period, there has been
relatively little work studying the phenomenologies associated with their
non-supersymmetric counterparts. The primary reason for this relative lack of
attention is the fact that strings without spacetime supersymmetry are
generally unstable, exhibiting large one-loop dilaton tadpoles. In this paper,
we demonstrate that this hurdle can be overcome in a class of tachyon-free
four-dimensional string models realized through coordinate-dependent
compactifications. Moreover, as we shall see, it is possible to construct
models in this class whose low-lying states resemble the Standard Model (or
even potential unified extensions thereof) --- all without any light
superpartners, and indeed without supersymmetry at any energy scale. The
existence of such models thus opens the door to general studies of
non-supersymmetric string phenomenology, and in this paper we proceed to
discuss a variety of theoretical and phenomenological issues associated with
such non-supersymmetric strings. On the theoretical side, we discuss the
finiteness properties of such strings, the general characteristics of their
mass spectra, the magnitude and behavior of their one-loop cosmological
constants, and their interpolation properties. By contrast, on the
phenomenological side, the properties we discuss are more model-specific and
include their construction techniques, their natural energy scales, their
particle and charge assignments, and the magnitudes of their associated Yukawa
couplings and scalar masses.
|
hep-th
|
Clock Fields and Logarithmic Decay of Dark Energy: We investigate the physical measurability of the infrared instability of a de
Sitter phase in the formalism recently proposed by Kitamoto et al.. We find
that the logarithmic decay of the effective cosmological constant is only
measurable if an additional clock field is introduced.
|
hep-th
|
All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops: We give a closed-form, prescriptive representation of all-multiplicity
two-loop MHV amplitude integrands in fully-color-dressed (non-planar) maximally
supersymmetric Yang-Mills theory.
|
hep-th
|
Slowly rotating Einstein-Maxwell-dilaton black hole and some aspects of
its thermodynamics: A slowly rotating black hole solution in Einstein-Maxwell-dilaton gravity was
considered. Having used the obtained solution we investigated thermodynamic
functions such as black hole's temperature, entropy and heat capacity. In
addition to examine thermodynamic properties of the black hole extended
technique was applied. The equation of state of Van der Waals type was obtained
and investigated. It has been shown that the given system has phase transitions
of the first as well as of the zeroth order for the temperatures below a
critical one which is notable feature of the black hole. A coexistence relation
for two phases was also considered and latent heat was calculated. In the end,
critical exponents were calculated.
|
hep-th
|
Celestial Klein Spaces: We consider the analytic continuation of $(p+q)$-dimensional Minkowski space
(with $p$ and $q$ even) to $(p,q)$-signature, and study the conformal boundary
of the resulting "Klein space". Unlike the familiar $(-+++..)$ signature, now
the null infinity ${\mathcal I}$ has only one connected component. The spatial
and timelike infinities ($i^0$ and $i'$) are quotients of generalizations of
AdS spaces to non-standard signature. Together, ${\mathcal I}, i^0$ and $i'$
combine to produce the topological boundary $S^{p+q-1}$ as an $S^{p-1} \times
S^{q-1}$ fibration over a null segment. The highest weight states (the
$L$-primaries) and descendants of $SO(p,q)$ with integral weights give rise to
natural scattering states. One can also define $H$-primaries which are highest
weight with respect to a signature-mixing version of the Cartan-Weyl generators
that leave a point on the celestial $S^{p-1} \times S^{q-1}$ fixed. These
correspond to massless particles that emerge at that point and are Mellin
transforms of plane wave states.
|
hep-th
|
Twist Quantization of String and B Field Background: In a previous paper, we investigated the Hopf algebra structure in string
theory and gave a unified formulation of the quantization of the string and the
space-time symmetry. In this paper, this formulation is applied to the case
with a nonzero B-field background, and the twist of the Poincare symmetry is
studied. The Drinfeld twist accompanied by the B-field background gives an
alternative quantization scheme, which requires a new normal ordering. In order
to obtain a physical interpretation of this twisted Hopf algebra structure, we
propose a method to decompose the twist into two successive twists and we give
two different possibilities of decomposition. The first is a natural
decomposition from the viewpoint of the twist quantization, leading to a new
type of twisted Poincare symmetry. The second decomposition reveals the
relation of our formulation to the twisted Poincare symmetry on the Moyal type
noncommutative space.
|
hep-th
|
On string theory on AdS$_3\times {M}_7$ in the tensionless limit: We review old and recent results on a special limit of string theory on
AdS$_3\times M_7$ with pure NS-NS fluxes: the limit in which the string length
$\ell_s=\sqrt{\alpha'}$ equals the AdS$_3$ radius $R $. At this point of the
moduli space, the theory exhibits special properties, which we discuss. Special
attention is focused on features of correlation functions that are related to
the non-compactness of the boundary CFT target space, and on how these features
change when the point $k\equiv R^2/\alpha ' =1$ is approached. Also, we briefly
review recent proposals for exact realizations of AdS/CFT correspondence at
this special point. \[\] This is the transcript of the talk delivered by the
author at the 8$^{\text{th}}$ edition of the Quantum Gravity in the Southern
Cone conference, held in Patagonia, December 16$^{\text{th}}$ -
20$^{\text{th}}$, 2019.
|
hep-th
|
Release of physical modes from unphysical fields: We present a basic idea and a toy model that physical modes originate from
unobservable fields. The model is defined on a higher-dimensional space-time
and has fermionic symmetries that make fields unphysical, and observable modes
can appear through a dimensional reduction.
|
hep-th
|
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