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hep-th/9112013
|
Matrix models of 2d gravity
|
These are introductory lectures for a general audience that give an overview
of the subject of matrix models and their application to random surfaces, 2d
gravity, and string theory. They are intentionally 1.5 years out of date.
0. Canned Diatribe, Introduction, and Apologies
1. Discretized surfaces, matrix models, and the continuum limit
2. All genus partition functions
3. KdV equations and other models
4. Quick tour of Liouville theory
| 1991-12-06
| 2007-05-23
|
[
"hep-th"
] |
P. Ginsparg
|
hep-th/9112011
|
Modular invariance and nonrenormalizable interactions
|
We examine the modular properties of nonrenormalizable superpotential terms
in string theory and show that the requirement of modular invariance
necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In
a class of models (free fermionic formulation) we explicitly verify that the
nontrivial structure imposed by the modular invariance is indeed present.
Alternatively, we argue that after proper field redefinition, nonrenormalizable
terms can be recast as to display their invariance under the modular group. We
also discuss the phenomenological implications of the above observations.
| 1991-12-05
| 2009-10-22
|
[
"hep-th"
] |
S. Kalara, J. Lopez, and D. Nanopoulos
|
hep-th/9112012
|
N=2 topological gauge theory, the Euler characteristic of moduli spaces,
and the Casson invariant
|
We discuss gauge theory with a topological N=2 symmetry. This theory captures
the de Rham complex and Riemannian geometry of some underlying moduli space
$\cal M$ and the partition function equals the Euler number of $\cal M$. We
explicitly deal with moduli spaces of instantons and of flat connections in two
and three dimensions.
To motivate our constructions we explain the relation between the
Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a
new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi
equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point
of view and relate them to supersymmetric quantum mechanics on spaces of
connections. As a consequence of these considerations we propose the Euler
number of the moduli space of flat connections as a generalization to arbitrary
three-manifolds of the Casson invariant. We also comment on the possibility of
constructing a topological version of the Penner matrix model.
| 1991-12-05
| 2016-03-23
|
[
"hep-th"
] |
Matthias Blau and George Thompson
|
hep-th/9112010
|
Harmonic Space, Self-Dual Yang Mills and the $N=2$ String
|
The geometrical structure and the quantum properties of the recently proposed
harmonic space action describing self-dual Yang-Mills (SDYM) theory are
analyzed. The geometrical structure that is revealed is closely related to the
twistor construction of instanton solutions. The theory gets no quantum
corrections and, despite having SDYM as its classical equation of motion, its S
matrix is trivial. It is therefore NOT the theory of the N=2 string. We also
discuss the 5-dimensional actions that have been proposed for SDYM.
| 1991-12-05
| 2009-09-29
|
[
"hep-th"
] |
Neil Marcus, Yaron Oz and Shimon Yankielowicz
|
hep-th/9112009
|
Nonlinear $\hat{W}_{\infty}$ Current Algebra in the SL(2,R)/U(1) Coset
Model
|
Previously we have established that the second Hamiltonian structure of the
KP hierarchy is a nonlinear deformation, called $\hat{W}_{\infty}$, of the
linear, centerless $W_{\infty}$ algebra. In this letter we present a free-field
realization for all generators of $\hat{W}_{\infty}$ in terms of two scalars as
well as an elegant generating function for the $\hat{W}_{\infty}$ currents in
the classical conformal $SL(2,R)/U(1)$ coset model. After quantization, a
quantum deformation of $\hat{W}_{\infty}$ appears as the hidden current algebra
in this model. The $\hat{W}_{\infty}$ current algebra results in an infinite
set of commuting conserved charges, which might give rise to $W$-hair for the
2d black hole arising in the corresponding string theory at level $k=9/4$.
| 1991-12-04
| 2019-06-05
|
[
"hep-th"
] |
Feng Yu and Yong-Shi Wu
|
hep-th/9112007
|
Exact s-Matrices for the Nonsimply-Laced Affine Toda Theories
$a_{2n-1}^{(2)}$
|
We derive the exact, factorized, purely elastic scattering matrices for the
$a_{2n-1}^{(2)}$ family of nonsimply-laced affine Toda theories. The derivation
takes into account the distortion of the classical mass spectrum by radiative
correction, as well as modifications of the usual bootstrap assumptions since
for these theories anomalous threshold singularities lead to a displacement of
some single particle poles.
| 1991-12-04
| 2009-10-22
|
[
"hep-th"
] |
G.W. Delius, M.T. Grisaru and D. Zanon
|
hep-th/9112008
|
Black Holes in Magnetic Monopoles
|
We study magnetically charged classical solutions of a spontaneously broken
gauge theory interacting with gravity. We show that nonsingular monopole
solutions exist only if the Higgs vacuum expectation value $v$ is less than or
equal to a critical value $v_{cr}$, which is of the order of the Planck mass.
In the limiting case the monopole becomes a black hole, with the region outside
the horizon described by the critical Reissner-Nordstrom solution. For
$v<v_{cr}$, we find additional solutions which are singular at $r=0$, but which
have this singularity hidden within a horizon. These have nontrivial matter
fields outside the horizon, and may be interpreted as small black holes lying
within a magnetic monopole. The nature of these solutions as a function of $v$
and of the total mass $M$ and their relation to the Reissner-Nordstrom
solutions is discussed.
| 1991-12-04
| 2009-10-22
|
[
"hep-th"
] |
K.Lee, V.P.Nair and Erick J.Weinberg
|
hep-th/9112006
|
Classification of Ten-Dimensional Heterotic Strings
|
Progress towards the classification of the meromorphic $c=24$ conformal field
theories is reported. It is shown if such a theory has any spin-1 currents, it
is either the Leech lattice CFT, or it can be written as a tensor product of
Kac-Moody algebras with total central charge 24. The total number of
combinations of Kac-Moody algebras for which meromorphic $c=24$ theories may
exist is 221. The next step towards classification is to obtain all modular
invariant combinations of Kac-Moody characters. The presently available results
are sufficient to obtain a complete list of all ten-dimensional heterotic
strings. Furthermore there are strong indications for the existence of several
(probably at least 20) new meromorphic $c=24$ theories.
| 1991-12-04
| 2009-10-22
|
[
"hep-th"
] |
A.N. Schellekens
|
hep-th/9112002
|
Homological (ghost) approach to constrained Hamiltonian systems
|
A survey of ghost techniques in mathematical physics, which can be grouped
under the rubric of `cohomological physics', particularly BRST cohomology.
| 1991-12-03
| 2008-02-03
|
[
"hep-th",
"math.QA"
] |
Jim Stasheff
|
hep-th/9112003
|
Non-perturbative Aspect of Zero Dimensional Supersring
|
We discuss the non-perturbative aspect of zero dimensional superstring. The
perturbative expansions of correlation functions diverge as
$\sum_l(3l)!\kappa^{2l}$, where $\kappa$ is a string coupling constant. This
implies there are non-perturbative contributions of order $\e^{C\kappa^{-{2
\over 3}}}$. (Here $C$ is a constant.) This situation contrasts with those of
critical or non-critical bosonic strings, where the perturbative expansions
diverge as $\sum_ll!\kappa^{2l}$ and non-perturbative behaviors go as
$\e^{C\kappa^{-1}}$. It is explained how such nonperturbative effects of order
$\e^{C\kappa^{-{2 \over 3}}}$ appear in zero dimensional superstring theory.
Due to these non-perturbative effects, the supersymmetry in target space breaks
down spontaneously.
| 1991-12-03
| 2007-05-23
|
[
"hep-th"
] |
Shin'ichi Nojiri
|
hep-th/9112004
|
Dilaton, winding modes and cosmological solutions
|
We review some formal aspects of cosmological solutions in closed string
theory with duality symmetric ``matter'' following recent paper with C. Vafa
(HUTP-91/A049). We consider two models : when the matter action is the
classical action of the fields corresponding to momentum and winding modes and
when the matter action is represented by the quantum vacuum energy of the
string compactified on a torus. Assuming that the effective vacuum energy is
positive one finds that in both cases the scale factor undergoes oscillations
from maximal to minimal values with the amplitude of oscillations decreasing to
zero or increasing to infinity depending on whether the effective coupling
(dilaton field) decreases or increases with time. The contribution of the
winding modes to the classical action prevents infinite expansion. Duality is
``spontaneously broken'' on a solution with generic initial conditions.
| 1991-12-03
| 2010-04-06
|
[
"hep-th"
] |
A.A. Tseytlin
|
hep-th/9112005
|
Path Integral Over Conformally Self-Dual Geometries
|
The path integral of four dimensional quantum gravity is restricted to
conformally self-dual metrics. It reduces to integrals over the conformal
factor and over the moduli space of conformally self--dual metrics and can be
studied with the methods of two dimensional quantum gravity in conformal gauge.
The conformal anomaly induces an analog of the Liouville action. The proposal
of David, Distler and Kawai is generalized to four dimensions. Critical
exponents and the analog of the c=1 barrier of two dimensional gravity are
derived. Connections with Weyl gravity and four dimensional topological gravity
are suggested.
| 1991-12-03
| 2014-11-18
|
[
"hep-th"
] |
Christof Schmidhuber (Caltech)
|
hep-th/9112001
|
Perturbations of a Stringy Black Hole
|
We extend the three dimensional stringy black hole of Horne and Horowitz to
four dimensions. After a brief discussion of the global properties of the
metric, we discuss the stability of the background with respect to small
perturbations, following the methods of Gilbert and of Chandrasekhar. The
potential for axial perturbations is found to be positive definite.
| 1991-12-02
| 2009-10-22
|
[
"hep-th"
] |
E. Raiten
|
hep-th/9111064
|
On Loop Equations In KdV Exactly Solvable String Theory
|
The non-perturbative behaviour of macroscopic loop amplitudes in the exactly
solvable string theories based on the KdV hierarchies is considered. Loop
equations are presented for the real non-perturbative solutions living on the
spectral half-line, allowed by the most general string equation
$[\tilde{P},Q]=Q$, where $\tilde{P}$ generates scale transformations. In
general the end of the half-line (the `wall') is a non-perturbative parameter
whose r\^ole is that of boundary cosmological constant. The properties are
compared with the perturbative behaviour and solutions of $[P,Q]=1$. Detailed
arguments are given for the $(2,2m-1)$ models while generalisation to the other
$(p,q)$ minimal models and $c=1$ is briefly addressed.
| 1991-11-30
| 2010-11-01
|
[
"hep-th"
] |
Simon Dalley
|
hep-th/9111060
|
Self-avoiding effective strings in lattice gauge theories
|
It is shown that the effective string recently introduced to describe the
long distance dynamics of 3D gauge systems in the confining phase has an
intriguing description in terms of models of 2D self-avoiding walks in the
dense phase. The deconfinement point, where the effective string becomes N=2
supersymmetric, may then be interpreted as the tricritical Theta point where
the polymer chain undergoes a collapse transition. As a consequence, a
universal value of the deconfinement temperature is predicted.
| 1991-11-28
| 2009-10-22
|
[
"hep-th"
] |
M. Caselle and F. Gliozzi
|
hep-th/9111061
|
c=5/2 Free Fermion Model of WB_{2} Algebra
|
We investigate the explicit construction of the $WB_{2}$ algebra, which is
closed and associative for all values of the central charge $c$, using the
Jacobi identity and show the agreement with the results studied previously.
Then we illustrate a realization of $c=\frac{5}{2}$ free fermion model, which
is $m \rightarrow \infty$ limit of unitary minimal series, $c ( WB_{2}
)=\frac{5}{2} (1-\frac{12}{ (m+3)(m+4) })$ based on the cosets $( \hat{B_{2}}
\oplus \hat{B_{2}}, \hat{B_{2} })$ at level $(1,m).$ We confirm by explicit
computations that the bosonic currents in the $ WB_{2}$ algebra are indeed
given by the Casimir operators of $\hat{B_{2}}$ .
| 1991-11-28
| 2015-06-26
|
[
"hep-th"
] |
Changhyun Ahn
|
hep-th/9111056
|
Evanescent Black Holes
|
A renormalizable theory of quantum gravity coupled to a dilaton and conformal
matter in two space-time dimensions is analyzed. The theory is shown to be
exactly solvable classically. Included among the exact classical solutions are
configurations describing the formation of a black hole by collapsing matter.
The problem of Hawking radiation and backreaction of the metric is analyzed to
leading order in a $1/N$ expansion, where $N$ is the number of matter fields.
The results suggest that the collapsing matter radiates away all of its energy
before an event horizon has a chance to form, and black holes thereby disappear
from the quantum mechanical spectrum. It is argued that the matter
asymptotically approaches a zero-energy ``bound state'' which can carry global
quantum numbers and that a unitary $S$-matrix including such states should
exist.
| 1991-11-28
| 2009-09-17
|
[
"hep-th"
] |
C. Callan, S. Giddings, J. Harvey and A. Strominger
|
hep-th/9111062
|
On the classification of quantum W-algebras
|
In this paper we consider the structure of general quantum W-algebras. We
introduce the notions of deformability, positive-definiteness, and reductivity
of a W-algebra. We show that one can associate a reductive finite Lie algebra
to each reductive W-algebra. The finite Lie algebra is also endowed with a
preferred $sl(2)$ subalgebra, which gives the conformal weights of the
W-algebra. We extend this to cover W-algebras containing both bosonic and
fermionic fields, and illustrate our ideas with the Poisson bracket algebras of
generalised Drinfeld-Sokolov Hamiltonian systems. We then discuss the
possibilities of classifying deformable W-algebras which fall outside this
class in the context of automorphisms of Lie algebras. In conclusion we list
the cases in which the W-algebra has no weight one fields, and further, those
in which it has only one weight two field.
| 1991-11-28
| 2009-10-22
|
[
"hep-th"
] |
P. Bowcock and G Watts
|
hep-th/9111059
|
N=2 String as a Topological Conformal Algebra
|
We prove that critical and subcritical N=2 string theory gives a realization
of an N=2 superfield extension of the topological conformal algebra. The
essential observation is the vanishing of the background charge.
| 1991-11-28
| 2009-10-22
|
[
"hep-th"
] |
J. Gomis and H. Suzuki
|
hep-th/9111063
|
Three Dimensional Chern-Simons Theory as a Theory of Knots and Links
|
Three dimensional SU(2) Chern-Simons theory has been studied as a topological
field theory to provide a field theoretic description of knots and links in
three dimensions. A systematic method has been developed to obtain the
link-invariants within this field theoretic framework. The monodromy properties
of the correlators of the associated Wess-Zumino SU(2)$_k$ conformal field
theory on a two-dimensional sphere prove to be useful tools. The method is
simple enough to yield a whole variety of new knot invariants of which the
Jones polynomials are the simplest example.
| 1991-11-28
| 2009-10-22
|
[
"hep-th",
"math.QA"
] |
R. K. Kaul and T. R. Govindarajan
|
hep-th/9111058
|
Unitary Representations of $W$ Infinity Algebras
|
We study the irreducible unitary highest weight representations, which are
obtained from free field realizations, of $W$ infinity algebras ($W_{\infty}$,
$W_{1+\infty}$, $W_{\infty}^{1,1}$, $W_{\infty}^M$, $W_{1+\infty}^N$,
$W_{\infty}^{M,N}$) with central charges ($2$, $1$, $3$, $2M$, $N$, $2M+N$).
The characters of these representations are computed. We construct a new
extended superalgebra $W_{\infty}^{M,N}$, whose bosonic sector is
$W_{\infty}^M\oplus W_{1+\infty}^N$. Its representations obtained from a free
field realization with central charge $2M+N$, are classified into two classes:
continuous series and discrete series. For the former there exists a
supersymmetry, but for the latter a supersymmetry exists only for $M=N$.
| 1991-11-28
| 2009-10-22
|
[
"hep-th",
"math.QA"
] |
Satoru Odake
|
hep-th/9111057
|
General Neveu-Schwarz Correlators in Super Liouville Theory
|
In this paper we compute the N-point correlation functions of the tachyon
operator from the Neveu Schwarz sector of super Liouville theory coupled to
matter fields (with $\hat c\le 1$) in the super Coulomb gas formulation, on
world sheets with spherical topology. We first integrate over the zero mode
assuming that the $s$ parameter takes an integer value, subsequently we
continue the parameter to an arbitrary real number. We included an arbitrary
number of screening charges (s.c.) and as a result, after renormalizing the
s.c., the external legs and the cosmological constant, the form of the final
amplitudes do not modify. Remarkably, the result is completely parallel to the
bosonic case. We also completed a discussion on the calculation of bosonic
correlators including arbitrary screening charges.
| 1991-11-27
| 2007-05-23
|
[
"hep-th"
] |
E. Abdalla, M.C.B. Abdalla, D. Dalmazi, Koji Harada
|
hep-th/9111055
|
Three Dimensional Periodic $U(1)$ Gauge Theory and Strings
|
It will be argued that among the known systems in three dimensions that have
string like excitations periodic U(1) pure gauge theories are the most likely
candidates to lead to a string representation of their universal properties.
Some recent work with F. David will also be reviewed.
| 1991-11-26
| 2009-10-22
|
[
"hep-th"
] |
H. Neuberger
|
hep-th/9111049
|
Operator Product Expansion and Topological States in $c = 1$ Matter
Coupled to 2-D Gravity
|
Factorization of the $N$-tachyon amplitudes in two-dimensional $c=1$ quantum
gravity is studied by means of the operator product expansion of vertex
operators after the Liouville zero mode integration. Short-distance
singularities between two tachyons with opposite chiralities account for all
singularities in the $N$-tachyon amplitudes. Although the factorization is
valid, other possible short-distance singularities corresponding to other
combinations of vertex operators are absent since the residue vanishes. Apart
from the tachyon states, there are infinitely many topological states
contributing to the intermediate states. This is a more detailed account of our
short communication on the factorization.
| 1991-11-25
| 2008-11-26
|
[
"hep-th"
] |
Norisuke Sakai and Yoshiaki Tanii
|
hep-th/9111051
|
Kontsevich - Miwa Transform of the Virasoro Constraints as Null-Vector
Decoupling Equations
|
We use the Kontsevich--Miwa transform to relate the Virasoro constraints on
integrable hierarchies with the David-Distler-Kawai formalism of
gravity-coupled conformal theories. The derivation relies on evaluating the
energy-momentum tensor on the hierarchy at special values of the spectral
parameter. We thus obtain in the Kontsevich parametrization the `master
equations' which implement the Virasoro constraints and at the same time
coincide with null-vector decoupling equations in an `auxiliary' conformal
field theory on the complex plane of the spectral parameter. This gives the
operators their gravitational scaling dimensions (for one out of four
possibilities to choose signs), with the $\alpha_+$ being equal to the
background charge $Q$ of an abstract $bc$ system underlying the structure of
the Virasoro constraints. The formalism also generalizes to the $N$-KdV
hierarchies.
| 1991-11-25
| 2008-02-03
|
[
"hep-th"
] |
A.M.Semikhatov
|
hep-th/9111050
|
On Moduli Space of C=0 Topological Conformal Field Theories
|
We studied the marginal deformation of the $c=0$ topological conformal field
theories (TCFT). We showed that topological $SL(2)$ Wess-Zumino-Witten (WZW)
model, topological superconformal ghost system, TCFT constructed from the $N=2$
superconformal system and two dimensional topological gravity belong to the
same one parameter family (moduli space) of the $c=0$ TCFT's. We conjectured
that the $N=2$ TCFT constructed from the Wolf space realization of $N=4$
superconformal algebra belongs to another family.
| 1991-11-25
| 2009-10-22
|
[
"hep-th"
] |
Hisahiro Yoshii
|
hep-th/9111052
|
On Black Holes In String Theory
|
In these lecture notes from Strings `91, I briefly sketch the analogy between
two dimensional black holes and the s-wave sector of four dimensional black
holes, and the physical interest of the latter, particularly in the
magnetically charged case.
| 1991-11-25
| 2012-06-03
|
[
"hep-th"
] |
Edward Witten
|
hep-th/9111054
|
The Super W_\INFTY Symmetry of the Manin-Radul Super KP Hierarchy
|
We show that the Manin-Radul super KP hierarchy is invariant under super
W_\infty transformations. These transformations are characterized by time
dependent flows which commute with the usual flows generated by the conserved
quantities of the super KP hierarchy.
| 1991-11-25
| 2008-11-26
|
[
"hep-th"
] |
A. Das, E. Sezgin and S.J. Sin
|
hep-th/9111053
|
Quantum Mechanics on the Circle and W_{1+\INFTY}
|
The algebra W_{1+\infty} with central charge c=0 can be identified with the
algebra of quantum observables of a particle moving on a circle.
Mathematically, it is the universal enveloping algebra of the Euclidean algebra
in two dimensions. Similarly, the super W_\infty algebra is found to be the
universal enveloping algebra of the super-Euclidean algebra in two dimensions.
| 1991-11-25
| 2009-10-22
|
[
"hep-th"
] |
R. Floreanini, R. Percacci and E. Sezgin
|
hep-th/9111047
|
The generalized no-ghost theorem for N=2 SUSY critical strings
|
We prove the no-ghost theorem for the N=2 SUSY strings in (2,2) dimensional
flat Minkowski space. We propose a generalization of this theorem for an
arbitrary geometry of the N=2 SUSY string theory taking advantage of the N=4
SCA generators present in this model. Physical states are found to be the
highest weight states of the N=4 SCA.
| 1991-11-23
| 2009-10-22
|
[
"hep-th"
] |
Jadwiga Bienkowska
|
hep-th/9111048
|
Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter
|
All solvable two-dimensional quantum gravity models have non-trivial BRST
cohomology with vanishing ghost number. These states form a ring and all the
other states in the theory fall into modules of this ring. The relations in the
ring and in the modules have a physical interpretation. The existence of these
rings and modules leads to nontrivial constraints on the correlation functions
and goes a long way toward solving these theories in the continuum approach.
| 1991-11-23
| 2009-09-15
|
[
"hep-th"
] |
D. Kutasov, E. Martinec and N. Seiberg
|
hep-th/9111046
|
On the classical $W_N^{(l)}$ algebras
|
We analyze the W_N^l algebras according to their conjectured realization as
the second Hamiltonian structure of the integrable hierarchy resulting from the
interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3
algebra is derived explicitly along these lines, thus providing further support
for the conjecture. This algebra is found to be equivalent to that obtained by
the method of Hamiltonian reduction. Furthermore, its twisted version
reproduces the algebra associated to a certain non-principal embedding of sl(2)
into sl(4), or equivalently, the u(2) quasi-superconformal algebra. The general
aspects of the W_N^l algebras are also presented.
| 1991-11-22
| 2015-06-26
|
[
"hep-th"
] |
D.A.Depireux, P.Mathieu
|
hep-th/9111045
|
A Classical Instability of Reissner-Nordstrom Solutions and the Fate of
Magnetically Charged Black Holes
|
Working in the context of spontaneously broken gauge theories, we show that
the magnetically charged Reissner-Nordstrom solution develops a classical
instability if the horizon is sufficiently small. This instability has
significant implications for the evolution of a magnetically charged black
hole. In particular, it leads to the possibility that such a hole could
evaporate completely, leaving in its place a nonsingular magnetic monopole.
| 1991-11-22
| 2009-10-22
|
[
"hep-th"
] |
K.Lee, V.P.Nair and E.J.Weinberg
|
hep-th/9111044
|
Modified Black Holes in Two Dimensional Gravity
|
The $SL(2,R)/U(1)$ gauged WZWN model is modified by a topological term and
the accompanying change in the geometry of the two dimensional target space is
determined. The possibility of this additional term arises from a symmetry in
the general formalism of gauging an isometry subgroup of a non-linear sigma
model with an antisymmetric tensor. It is shown, in particular, that the
space-time exhibits some general singularities for which the recently found
black hole is just a special case. From a conformal field theory point of view
and for special values of the unitary representations of $SL(2,R)$, this
topological term can be interpreted as a small perturbation by a (1,1)
conformal operator of the gauged WZWN action.
| 1991-11-22
| 2009-10-22
|
[
"hep-th"
] |
N. Mohammedi
|
hep-th/9111041
|
Instabilities in the gravitational background and string theory
|
We indicate the tentative source of instability in the two-dimensional black
hole background. There are relevant operators among the tachyon and the higher
level vertex operators in the conformal field theory. Connection of this
instability with Hawking radiation is not obvious. The situation is somewhat
analogous to fields in the background of a negative mass Euclidean
Schwarzschild solution (in four dimensions). Speculation is made about decay of
the Minkowski black hole into finite temperature flat space.
| 1991-11-21
| 2007-05-23
|
[
"hep-th"
] |
Anirvan M. Sengupta
|
hep-th/9111042
|
"the Instability of String-Theoretic Black Holes"
|
It is demonstrated that static, charged, spherically--symmetric black holes
in string theory are classically and catastrophically unstable to linearized
perturbations in four dimensions, and moreover that unstable modes appear for
arbitrarily small positive values of the charge. This catastrophic classical
instability dominates and is distinct from much smaller and less significant
effects such as possible quantum mechanical evaporation. The classical
instability of the string--theoretic black hole contrasts sharply with the
situation which obtains for the Reissner--Nordstr\"om black hole of general
relativity, which has been shown by Chandrasekhar to be perfectly stable to
linearized perturbations at the event horizon.
| 1991-11-21
| 2007-05-23
|
[
"hep-th"
] |
Gerald Gilbert (umdhep.umd.edu)
|
hep-th/9111043
|
An introduction to quantized Lie groups and algebras
|
We give a selfcontained introduction to the theory of quantum groups
according to Drinfeld highlighting the formal aspects as well as the
applications to the Yang-Baxter equation and representation theory.
Introductions to Hopf algebras, Poisson structures and deformation quantization
are also provided. After having defined Poisson-Lie groups we study their
relation to Lie-bi algebras and the classical Yang-Baxter equation. Then we
explain in detail the concept of quantization for them. As an example the
quantization of $sl_2$ is explicitly carried out. Next we show how quantum
groups are related to the Yang-Baxter equation and how they can be used to
solve it. Using the quantum double construction we explicitly construct the
universal $R$-matrix for the quantum $sl_2$ algebra. In the last section we
deduce all finite dimensional irreducible representations for $q$ a root of
unity. We also give their tensor product decomposition (fusion rules) which is
relevant to conformal field theory.
| 1991-11-21
| 2009-10-22
|
[
"hep-th"
] |
T.Tjin
|
hep-th/9111036
|
Dressing Symmetries
|
We study Lie-Poisson actions on symplectic manifolds. We show that they are
generated by non-Abelian Hamiltonians. We apply this result to the group of
dressing transformations in soliton theories; we find that the non-Abelian
Hamiltonian is just the monodromy matrix. This provides a new proof of their
Lie-Poisson property. We show that the dressing transformations are the
classical precursors of the non-local and quantum group symmetries of these
theories. We treat in detail the examples of the Toda field theories and the
Heisenberg model.
| 1991-11-20
| 2008-11-26
|
[
"hep-th"
] |
O. Babelon and D. Bernard
|
hep-th/9111040
|
A Superstring Theory in Four Curved Space-Time Dimensions
|
Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four
dimensional curved space-time are constructed as exact $N=1$ superconformal
theories. The tachyon is eliminated with a GSO projection. The theory is based
on the N=1 superconformal gauged WZW model for the anti-de Sitter coset
$SO(3,2)/SO(3,1)$ with integer central extension $k=5$. The model has dynamical
duality properties in its space-time metric that are similar to the large-small
($R\rightarrow 1/R$) duality of tori. To first order in a $1/k$ expansion we
give expressions for the metric, the dilaton, the Ricci tensor and their dual
generalizations. The curvature scalar has several singularities at various
locations in the 4-dimensional manifold. This provides a new singular solution
to Einstein's equations in the presence of matter in four dimensions. A
non-trivial path integral measure which we conjectured in previous work for
gauged WZW models is verified.
| 1991-11-20
| 2009-10-22
|
[
"hep-th"
] |
I. Bars and K. Sfetsos
|
hep-th/9111038
|
Charged Black Holes in Two-Dimensional String Theory
|
We discuss two dimensional string theories containing gauge fields introduced
either via coupling to open strings, in which case we get a Born-Infeld type
action, or via heterotic compactification. The solutions to the modified
background field equations are charged black holes which exhibit interesting
space-time geometries. We also compute their masses and charges.
| 1991-11-20
| 2011-07-19
|
[
"hep-th"
] |
Michael D. McGuigan, Chiara R. Nappi and Scott A. Yost
|
hep-th/9111035
|
Exact S-Matrix for 2D String Theory
|
We formulate simple graphical rules which allow explicit calculation of
nonperturbative $c=1$ $S$-matrices. This allows us to investigate the
constraint of nonperturbative unitarity, which indeed rules out some theories.
Nevertheless, we show that there is an infinite parameter family of
nonperturbatively unitary $c=1$ $S$-matrices. We investigate the dependence of
the $S$-matrix on one of these nonperturbative parameters. In particular, we
study the analytic structure, background dependence, and high-energy behavior
of some nonperturbative $c=1$ $S$-matrices. The scattering amplitudes display
interesting resonant behavior both at high energies and in the complex energy
plane.
| 1991-11-20
| 2011-04-05
|
[
"hep-th"
] |
Gregory Moore, M. Ronen Plesser, and Sanjaye Ramgoolam
|
hep-th/9111037
|
Unification of All String Models with $c<1$
|
A 1-matrix model is proposed, which nicely interpolates between
double-scaling continuum limits of all multimatrix models. The interpolating
partition function is always a KP $\tau $-function and always obeys ${\cal
L}_{-1}$-constraint and string equation. Therefore this model can be considered
as a natural unification of all models of 2d-gravity (string models) with
$c\leq 1.$
| 1991-11-20
| 2009-10-22
|
[
"hep-th"
] |
S.Kharchev, A.Marshakov, A.Mironov, A.Morozov, A.Zabrodin
|
hep-th/9111039
|
Matrix Models at Finite N
|
We summarize some aspects of matrix models from the approaches directly based
on their properties at finite N.
| 1991-11-20
| 2007-05-23
|
[
"hep-th"
] |
H. Itoyama
|
hep-th/9111034
|
Quantum W_3 Gravity
|
We briefly review some results in the theory of quantum $W_3$ gravity in the
chiral gauge. We compare them with similar results in the analogous but simpler
cases of $d=2$ induced gauge theories and $d=2$ induced gravity.
| 1991-11-19
| 2007-05-23
|
[
"hep-th"
] |
Kareljan Schoutens, Alexander Sevrin and Peter van Nieuwenhuizen
|
hep-th/9111033
|
Supermatrix Models
|
Random matrix models based on an integral over supermatrices are proposed as
a natural extension of bosonic matrix models. The subtle nature of superspace
integration allows these models to have very different properties from the
analogous bosonic models. Two choices of integration slice are investigated.
One leads to a perturbative structure which is reminiscent of, and perhaps
identical to, the usual Hermitian matrix models. Another leads to an eigenvalue
reduction which can be described by a two component plasma in one dimension. A
stationary point of the model is described.
| 1991-11-19
| 2015-06-26
|
[
"hep-th"
] |
Scott A. Yost
|
hep-th/9111031
|
On the Evaporation of Black Holes in String Theory
|
We show that, in string theory, the quantum evaporation and decay of black
holes in two-dimensional target space is related to imaginary parts in
higher-genus string amplitudes. These arise from the regularisation of modular
infinities due to the sum over world-sheet configurations, that are known to
express the instabilities of massive string states in general, and are not
thermal in character. The absence of such imaginary parts in the matrix model
limit confirms that the latter constitutes the final stage of the evaporation
process, at least in perturbation theory. Our arguments appear to be quite
generic, related only to the summation over world-sheet surfaces, and hence
should also apply to higher-dimensional target spaces.
| 1991-11-18
| 2009-09-11
|
[
"hep-th"
] |
J. Ellis, N. E. Mavromatos and D.V. Nanopoulos
|
hep-th/9111032
|
W-Algebra Symmetries of Generalised Drinfel'd-Sokolov Hierarchies
|
Using the zero-curvature formulation, it is shown that W-algebra
transformations are symmetries of corresponding generalised Drinfel'd-Sokolov
hierarchies. This result is illustrated with the examples of the KdV and
Boussinesque hierarchies, and the hierarchy associated to the
Polyakov-Bershadsky W-algebra.
| 1991-11-18
| 2009-10-22
|
[
"hep-th"
] |
B. Spence
|
hep-th/9111028
|
String field actions from W-infinity
|
Starting from $W_{\infty}$ as a fundamental symmetry and using the coadjoint
orbit method, we derive an action for one dimensional strings. It is shown that
on the simplest nontrivial orbit this gives the single scalar collective field
theory. On higher orbits one finds generalized KdV type field theories with
increasing number of components. Here the tachyon is coupled to higher tensor
fields.
| 1991-11-15
| 2009-10-22
|
[
"hep-th"
] |
Jean Avan and Antal Jevicki
|
hep-th/9111030
|
Comments on Supersymmetric Vector and Matrix Models
|
Some results in random matrices are generalized to supermatrices, in
particular supermatrix integration is reduced to an integration over the
eigenvalues and the resulting volume element is shown to be equivalent to a one
dimensional Coulomb gas of both positive and negative charges.It is shown
that,for polynomial potentials, after removing the instability due to the
annihilation of opposite charges, supermatrix models are indistinguishable from
ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and
Manes. It is pointed out however that this may not be true for more general
potentials such as for instance the supersymmetric generalization of the Penner
model.
| 1991-11-15
| 2010-04-06
|
[
"hep-th"
] |
A.D'adda
|
hep-th/9111027
|
Towards a Classification of Fusion Rule Algebras in Rational Conformal
Field Theories
|
We review the main topics concerning Fusion Rule Algebras (FRA) of Rational
Conformal Field Theories. After an exposition of their general properties, we
examine known results on the complete classification for low number of fields
($\leq 4$). We then turn our attention to FRA's generated polynomially by one
(real) fundamental field, for which a classification is known. Attempting to
generalize this result, we describe some connections between FRA's and Graph
Theory. The possibility to get new results on the subject following this
``graph'' approach is briefly discussed.
| 1991-11-15
| 2011-04-15
|
[
"hep-th"
] |
M.Caselle, G.Ponzano and F.Ravanini
|
hep-th/9111029
|
Isolated States and the Classical Phase Spase of 2-d String Theory
|
We investigate the classical phase space of 2-d string theory. We derive the
linearised covariant equations for the spacetime fields by considering the most
general deformation of the energy-momentum tensor which describes $c=1$ matter
system coupled to 2-d gravity and by demanding that it respect conformal
invariance. We derive the gauge invariances of the theory, and so investigate
the classical phase space, defined as the space of all solutions to the
equations of motion modulo gauge transformations. We thus clarify the origins
of two classes of isolated states.
| 1991-11-14
| 2009-10-22
|
[
"hep-th"
] |
Mark Evans and Ioannis Giannakis
|
hep-th/9111026
|
Critical Percolation in Finite Geometries
|
The methods of conformal field theory are used to compute the crossing
probabilities between segments of the boundary of a compact two-dimensional
region at the percolation threshold. These probabilities are shown to be
invariant not only under changes of scale, but also under mappings of the
region which are conformal in the interior and continuous on the boundary. This
is a larger invariance than that expected for generic critical systems.
Specific predictions are presented for the crossing probability between
opposite sides of a rectangle, and are compared with recent numerical work. The
agreement is excellent.
| 1991-11-14
| 2009-10-22
|
[
"hep-th"
] |
John Cardy
|
hep-th/9111025
|
Picard-Fuchs equations and mirror maps for hypersurfaces
|
We describe a strategy for computing Yukawa couplings and the mirror map,
based on the Picard-Fuchs equation. (Our strategy is a variant of the method
used by Candelas, de la Ossa, Green, and Parkes in the case of quintic
hypersurfaces.) We then explain a technique of Griffiths which can be used to
compute the Picard-Fuchs equations of hypersurfaces. Finally, we carry out the
computation for four specific examples (including quintic hypersurfaces,
previously done by Candelas et al.). This yields predictions for the number of
rational curves of various degrees on certain hypersurfaces in weighted
projective spaces. Some of these predictions have been confirmed by classical
techniques in algebraic geometry.
| 1991-11-12
| 2008-02-03
|
[
"hep-th",
"math.AG"
] |
David R. Morrison
|
hep-th/9111024
|
Ward Identities of Liouville Gravity coupled to Minimal Conformal Matter
|
The Ward identities of the Liouville gravity coupled to the minimal conformal
matter are investigated. We introduce the pseudo-null fields and the
generalized equations of motion, which are classified into series of the
Liouville charges. These series have something to do with the W and Virasoro
constraints. The pseudo-null fields have non-trivial contributions at the
boundaries of the moduli space. We explicitly evaluate the several boundary
contributions. Then the structures similar to the W and the Virasoro
constraints appearing in the topological and the matrix methods are realized.
Although our Ward identities have some different features from the other
methods, the solutions of the identities are consistent to the matrix model
results.
| 1991-11-12
| 2008-11-26
|
[
"hep-th"
] |
Ken-ji Hamada
|
hep-th/9111022
|
Restricted sine-Gordon Theory in the Repulsive Regime as Perturbed
Minimal CFTs
|
We construct the restricted sine-Gordon theory by truncating the sine-Gordon
multi-soliton Hilbert space for the repulsive coupling constant due to the
quantum group symmetry $SL_q(2)$ which we identify from the Korepin's
$S$-matrices. We connect this restricted sine-Gordon theory with the minimal
($c<1$) conformal field theory ${\cal M}_{p/p+2}$ ($p$ odd) perturbed by the
least relevent primary field $\Phi_{1,3}$. The exact $S$-matrices are derived
for the particle spectrum of a kink and neutral particles. As a consistency
check, we compute the central charge of the restricted theory in the UV limit
using the thermodynamic Bethe ansatz analysis and show that it is equal to that
of ${\cal M}_{p/p+2}$.
| 1991-11-11
| 2007-05-23
|
[
"hep-th"
] |
Changrim Ahn
|
hep-th/9111021
|
Bosonization of Nonrelativistic Fermions and W-infinity Algebra
|
We discuss the bosonization of non-relativistic fermions in one space
dimension in terms of bilocal operators which are naturally related to the
generators of $W$-infinity algebra. The resulting system is analogous to the
problem of a spin in a magnetic field for the group $W$-infinity. The new
dynamical variables turn out to be $W$-infinity group elements valued in the
coset $W$-infinity/$H$ where $H$ is a Cartan subalgebra. A classical action
with an $H$ gauge invariance is presented. This action is three-dimensional. It
turns out to be similiar to the action that describes the colour degrees of
freedom of a Yang-Mills particle in a fixed external field. We also discuss the
relation of this action with the one we recently arrived at in the Euclidean
continuation of the theory using different coordinates.
| 1991-11-11
| 2009-10-22
|
[
"hep-th"
] |
Sumit R. Das, Avinash Dhar, Gautam Mandal and Spenta R. Wadia
|
hep-th/9111023
|
Representation of Quantum Algebras and q-Special Functions
|
The connection between q-analogs of special functions and representations of
quantum algebras has been developed recently. It has led to advances in the
theory of q-special functions that we here review.
| 1991-11-11
| 2008-02-03
|
[
"hep-th",
"math.QA"
] |
R. Floreanini and L. Vinet
|
hep-th/9111018
|
N=2 Coset Compactifications with Non-Diagonal Invariants
|
We consider 4-dimensional string models obtained by tensoring N=2 coset
theories with non-diagonal modular invariants. We present results from a
systematic analysis including moddings by discrete symmetries.
| 1991-11-08
| 2009-03-27
|
[
"hep-th"
] |
G. Aldazabal, I. Allekotte, A. Font and C. Nunez
|
hep-th/9111020
|
Topological Landau-Ginzburg Matter from Sp(N)_{K} Fusion Rings
|
We find and analyze the Landau-Ginzburg potentials whose critical points
determine chiral rings which are exactly the fusion rings of Sp(N)_{K} WZW
models. The quasi-homogeneous part of the potential associated with Sp(N)_{K}
is the same as the quasi-homogeneous part of that associated with SU(N+1)_{K},
showing that these potentials are different perturbations of the same
Grassmannian potential. Twisted N=2 topological Landau-Ginzburg theories are
derived from these superpotentials. The correlation functions, which are just
the Sp(N)_{K} Verlinde dimensions, are expressed as fusion residues. We note
that the Sp(N)_{K} and Sp(K)_{N} topological Landau-Ginzburg theories are
identical, and that while the SU(N)_{K} and SU(K)_{N} topological
Landau-Ginzburg models are not, they are simply related.
| 1991-11-08
| 2009-10-22
|
[
"hep-th"
] |
Michelle Bourdeau, Eli J. Mlawer, Harold Riggs, and Howard J.
Schnitzer
|
hep-th/9111019
|
Physics Focus and Fiscal Forces
|
Two items are reproduced herein: my `Outlook' talk, an amended version of
which was presented at the 1991 joint Lepton--Photon and EPS Conference in
Geneva, and an Open Letter addressed to HEPAP. One is addressed primarily to
the European high--energy physics community, the other to the American. A
common theme of these presentations is a plea for the rational allocation of
the limited funds society provides for high--energy physics research. If my
`loose cannon' remarks may seem irresponsible to some of my colleagues, my
silence would be more so.
| 1991-11-08
| 2007-05-23
|
[
"hep-th"
] |
S. L. Glashow
|
hep-th/9111016
|
Exact Results for Supersymmetric Sigma Models
|
We show that the metric and Berry's curvature for the ground states of $N=2$
supersymmetric sigma models can be computed exactly as one varies the Kahler
structure. For the case of $CP^n$ these are related to special solutions of
affine toda equations. This allows us to extract exact results (including exact
instanton corrections). We find that the ground state metric is non-singular as
the size of the manifold shrinks to zero thus suggesting that 2d QFT makes
sense even beyond zero radius. In other words it seems that manifolds with zero
size are non-singular as target spaces for string theory (even when they are
not conformal). The cases of $CP^1$ and $CP^2$ are discussed in more detail.
| 1991-11-07
| 2009-10-22
|
[
"hep-th"
] |
S. Cecotti and C. Vafa
|
hep-th/9111014
|
Scattering and Thermodynamics of Fractionally-Charged Supersymmetric
Solitons
|
We show that there are solitons with fractional fermion number in integrable
$N$=2 supersymmetric models. We obtain the soliton S-matrix for the minimal,
$N$=2 supersymmetric theory perturbed in the least relevant chiral primary
field, the $\Phi _{(1,3)}$ superfield. The perturbed theory has a nice
Landau-Ginzburg description with a Chebyshev polynomial superpotential. We show
that the S-matrix is a tensor product of an associated ordinary $ADE$ minimal
model S-matrix with a supersymmetric part. We calculate the ground-state energy
in these theories and in the analogous $N$=1 case and $SU(2)$ coset models. In
all cases, the ultraviolet limit is in agreement with the conformal field
theory.
| 1991-11-07
| 2009-10-22
|
[
"hep-th"
] |
P. Fendley and K. Intriligator
|
hep-th/9111017
|
Topological Mirrors and Quantum Rings
|
Aspects of duality and mirror symmetry in string theory are discussed. We
emphasize, through examples, the importance of loop spaces for a deeper
understanding of the geometrical origin of dualities in string theory. Moreover
we show that mirror symmetry can be reformulated in very simple terms as the
statement of equivalence of two classes of topological theories: Topological
sigma models and topological Landau-Ginzburg models. Some suggestions are made
for generalization of the notion of mirror symmetry.
| 1991-11-07
| 2007-05-23
|
[
"hep-th"
] |
C. Vafa
|
hep-th/9111015
|
Differential Renormalization of the Wess-Zumino Model
|
We apply the recently developed method of differential renormalization to the
Wess-Zumino model. From the explicit calculation of a finite, renormalized
effective action, the $\beta$-function is computed to three loops and is found
to agree with previous existing results. As a further, nontrivial check of the
method, the Callan-Symanzik equations are also verified to that loop order.
Finally, we argue that differential renormalization presents advantages over
other superspace renormalization methods, in that it avoids both the
ambiguities inherent to supersymmetric regularization by dimensional reduction
(SRDR), and the complications of virtually all other supersymmetric regulators.
| 1991-11-07
| 2009-10-22
|
[
"hep-th"
] |
Peter E. Haagensen
|
hep-th/9111013
|
Extra States in C<1 String Theory
|
A construction of elements of the BRS cohomology of ghost number +/- 1 in c<1
string theory is described, and their two-point function computed on the
sphere. The construction makes precise the relation between these extra states
and null vectors. The physical states of ghost number +1 are found to be exact
forms with respect to a ``conjugate'' BRS operator.
| 1991-11-06
| 2007-05-23
|
[
"hep-th"
] |
Sunil Mukhi
|
hep-th/9111011
|
Intrinsic and extrinsic geometry of random surfaces
|
We prove that the extrinsic Hausdorff dimension is always greater than or
equal to the intrinsic Hausdorff dimension in models of triangulated random
surfaces with action which is quadratic in the separation of vertices. We
furthermore derive a few naive scaling relations which relate the intrinsic
Hausdorff dimension to other critical exponents. These relations suggest that
the intrinsic Hausdorff dimension is infinite if the susceptibility does not
diverge at the critical point.
| 1991-11-05
| 2009-10-22
|
[
"hep-th"
] |
Thordur Jonsson
|
hep-th/9111009
|
Geometry of Scattering at Planckian Energies
|
We present an alternative derivation and geometrical formulation of Verlinde
topological field theory, which may describe scattering at center of mass
energies comparable or larger than the Planck energy. A consistent trunckation
of 3+1 dimensional Einstein action is performed using the standard geometrical
objects, like tetrads and spin connections. The resulting topological invariant
is given in terms of differential forms.
| 1991-11-05
| 2009-10-22
|
[
"hep-th"
] |
Renata Kallosh
|
hep-th/9111012
|
Flows and Solitary Waves in Unitary Matrix Models with Logarithmic
Potentials
|
We investigate unitary one-matrix models coupled to bosonic quarks. We derive
a flow equation for the square-root of the specific heat as a function of the
renormalized quark mass. We show numerically that the flows have a finite
number of solitary waves, and we postulate that their number equals the number
of quark flavors. We also study the nonperturbative behavior of this theory and
show that as the number of flavors diverges, the flow does not reach
two-dimensional gravity.
| 1991-11-05
| 2009-10-22
|
[
"hep-th"
] |
Joseph A. Minahan
|
hep-th/9111010
|
D=10 supersymmetric chern-simons gauge theory
|
The Chern-Simons ten-dimensional manifestly supersymmetric non-Abelian gauge
theory is presented by performing the second quantization of the superparticle
theory. The equation of motion is $F = (d+A)^2 = 0$, where $d$ is the nilpotent
fermionic BRST operator of the first quantized theory and $A$ is the anti-
commuting connection for the gauge group. This equation can be derived as a
condition of the gauge independence of the first quantized theory in a
background field $A$, or from the string field theory Lagrangian of the Chern-
Simons type. The trivial solutions of the cohomology are the gauge symmetries,
the non-trivial solution is given by the D=10 superspace, describing the super
Yang-Mills theory on shell
| 1991-11-05
| 2007-05-23
|
[
"hep-th"
] |
R. Kallosh
|
hep-th/9111007
|
Polymers and percolation in two dimensions and twisted N=2 supersymmetry
|
It is shown how twisted N=2 (k=1) provides for the first time a complete
conformal field theory description of the usual geometrical phase transitions
in two dimensions, like polymers, percolation or brownian motion. In
particular, four point functions of operators with half integer Kac labels are
computed, together with geometrical operator products. In addition to Ramond
and Neveu Schwartz, a sector with quarter twists has to be introduced. The role
of fermions and their various sectors is geometrically interpreted, modular
invariant partition functions are built. The presence of twisted N=2 is traced
back to the Parisi Sourlas supersymmetry. It is shown that N=2 leads also to
new non trivial predictions; for instance the fractal dimension of the
percolation backbone in two dimensions is conjectured to be D=25/16, in good
agreement with numerical studies.
| 1991-11-04
| 2009-10-22
|
[
"hep-th"
] |
Hubert Saleur
|
hep-th/9111005
|
Quantum Harmonic Oscillator Algebra and Link Invariants
|
The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is
defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf
algebra we define an infinite dimensional braid group representation on the
Hilbert space of the harmonic oscillator, and an extended Yang--Baxter system
in the sense of Turaev. The corresponding link invariant is computed in some
particular cases and coincides with the inverse of the Alexander--Conway
polynomial. The $R$ matrix of $U_q (h_4)$ can be interpreted as defining a
baxterization of the intertwiners for semicyclic representations of $SU(2)_q$
at $q=e^{2 \pi i/N}$ in the $N \rightarrow \infty$ limit.Finally we define new
multicolored braid group representations and study their relation to the
multivariable Alexander--Conway polynomial.
| 1991-11-04
| 2008-02-03
|
[
"hep-th",
"math.QA"
] |
C. Gomez and G. Sierra
|
hep-th/9111006
|
Chern-Simons Dynamics and the Quantum Hall Effect
|
Theoretical developments during the past several years have shown that large
scale properties of the Quantum Hall system can be successfully described by
effective field theories which use the Chern-Simons interaction. In this
article, we first recall certain salient features of the Quantum Hall Effect
and their microscopic explanation. We then review one particular approach to
their description based on the Chern-Simons Lagrangian and its variants.
| 1991-11-04
| 2007-05-23
|
[
"hep-th"
] |
A. P. Balachandran and A.M. Srivastava
|
hep-th/9111008
|
Geometrical Lattice models for N=2 supersymmetric theories in two
dimensions
|
We introduce in this paper two dimensional lattice models whose continuum
limit belongs to the $N=2$ series. The first kind of model is integrable and
obtained through a geometrical reformulation, generalizing results known in the
$k=1$ case, of the $\Gamma_{k}$ vertex models (based on the quantum algebra
$U_{q}sl(2)$ and representation of spin $j=k/2$). We demonstrate in particular
that at the $N=2$ point, the free energy of the $\Gamma_{k}$ vertex model can
be obtained exactly by counting arguments, without any Bethe ansatz
computation, and we exhibit lattice operators that reproduce the chiral ring.
The second class of models is more adequately described in the language of
twisted $N=2$ supersymmetry, and consists of an infinite series of
multicritical polymer points, which should lead to experimental realizations.
It turns out that the exponents $\nu=(k+2)/2(k+1)$ for these multicritical
polymer points coincide with old phenomenological formulas due to the chemist
Flory. We therefore confirm that these formulas are {\bf exact} in two
dimensions, and suggest that their unexpected validity is due to non
renormalization theorems for the $N=2$ underlying theories. We also discuss the
status of the much discussed theta point for polymers in the light of $N=2$
renormalization group flows.
| 1991-11-04
| 2009-10-22
|
[
"hep-th"
] |
Hubert Saleur
|
hep-th/9111004
|
Chern-Simons Theory with Finite Gauge Group
|
These theories, which are surely some of the simplest possible quantum field
theories, were introduced in a paper of Dijkgraaf and Witten. The path integral
reduces to a finite sum, so it is quite amenable to direct mathematical study.
Although the theory exisits in arbitrary dimensions, it is most interesting in
$2+1$~dimensions, where it has a ``modular structure.'' This is related to
quantum groups, and the precise details may give clues as to what happens in
other contexts.
This paper is written using AMSTeX 2.1, which can be obtained via ftp from
the American Mathematical Society (instructions included). 1 encapsulated
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| 1991-11-03
| 2010-11-01
|
[
"hep-th",
"math.QA"
] |
Daniel S. Freed, Frank Quinn
|
hep-th/9111003
|
A Remark on Conformal Anomaly and Extrinsic Geometry of Random Surfaces
|
In low dimensions, conformal anomaly has profound influence on the critical
behavior of random surfaces with extrinsic curvature rigidity $1/\a$. We
illustrate this by making a small $D$ expansion of rigid random surfaces, where
a non-trivial infra-red fixed point is shown to exist. We speculate on the
renormalization group flow diagram in the $(\a,D)$ plane. We argue that the
qualitative behavior of numerical simulations in $D=3, 4$ could be understood
on the basis of the phase diagram.
| 1991-11-02
| 2008-11-26
|
[
"hep-th"
] |
Zhu Yang
|
hep-th/9111002
|
Anomaly Freedom and Realisations for Super-$W_3$ Strings
|
We construct new multi-field realisations of the $N=2$ super-$W_3$ algebra,
which are important for building super-$W_3$ string theories. We derive the
structure of the ghost vacuum for such theories, and use the result to
calculate the intercepts. These results determine the conditions for physical
states in the super-$W_3$ string theory.
| 1991-11-01
| 2009-10-07
|
[
"hep-th"
] |
H. Lu, C.N. Pope, X.J. Wang and K.W. Xu
|
hep-th/9111001
|
Topological Field Theories and Space-Time Singularity
|
Based on a study of recently proposed solution of 2 dim. black hole we argue
that the space-time singularities of general relativity may be described by
topological field theories (TFTs). We also argue that in general TFT is a field
theory which decsribes singular configurations with a reduced holonomy in its
field space.
| 1991-11-01
| 2009-10-22
|
[
"hep-th"
] |
Tohru Eguchi (Enrico Fermi Institute, University of Chicago and
Department of Physics, University of Tokyo)
|
hep-th/9110076
|
Non-Compact WZW Conformal Field Theories
|
We discuss non-compact WZW sigma models, especially the ones with symmetric
space $H^{\bf C}/H$ as the target, for $H$ a compact Lie group. They offer
examples of non-rational conformal field theories. We remind their relation to
the compact WZW models but stress their distinctive features like the
continuous spectrum of conformal weights, diverging partition functions and the
presence of two types of operators analogous to the local and non-local
insertions recently discussed in the Liouville theory. Gauging non-compact
abelian subgroups of $H^{\bf C}$ leads to non-rational coset theories. In
particular, gauging one-parameter boosts in the $SL(2,\bC)/SU(2)$ model gives
an alternative, explicitly stable construction of a conformal sigma model with
the euclidean 2D black hole target. We compute the (regularized) toroidal
partition function and discuss the spectrum of the theory. A comparison is made
with more standard approach based on the $U(1)$ coset of the $SU(1,1)$ WZW
theory where stability is not evident but where unitarity becomes more
transparent.
| 1991-10-31
| 2007-05-23
|
[
"hep-th"
] |
Krzysztof Gawedzki
|
hep-th/9110072
|
Conformal Edge Currents in Chern-Simons Theories
|
We develop elementary canonical methods for the quantization of abelian and
nonabelian Chern-Simons actions using well known ideas in gauge theories and
quantum gravity. Our approach does not involve choice of gauge or clever
manipulations of functional integrals. When the spatial slice is a disc, it
yields Witten's edge states carrying a representation of the Kac-Moody algebra.
The canonical expression for the generators of diffeomorphisms on the boundary
of the disc are also found, and it is established that they are the
Chern-Simons version of the Sugawara construction. This paper is a prelude to
our future publications on edge states, sources, vertex operators, and their
spin and statistics in 3D and 4D topological field theories.
| 1991-10-30
| 2015-06-26
|
[
"hep-th"
] |
A.P.Balachandran, G. Bimonte, K.S.Gupta and A. Stern
|
hep-th/9110073
|
The Covariant W_3 Action
|
Starting from SL(3,R) Chern-Simons theory we derive the covariant action for
W_3 gravity.
| 1991-10-30
| 2009-10-22
|
[
"hep-th"
] |
Jan de Boer and Jacob Goeree
|
hep-th/9110075
|
On N=2 strings and classical scattering solutions of self-dual
Yang-Mills in (2,2) spacetime
|
Ooguri and Vafa have shown that the open N=2 string corresponds to self-dual
Yang-Mills (SDYM) and also that, in perturbation theory, it has has a vanishing
four particle scattering amplitude. We discuss how the dynamics of the three
particle scattering implies that on shell states can only scatter if their
momenta lie in the same self-dual plane and then investigate classical SDYM
with the aim of comparing exact solutions with the tree level perturbation
theory predictions. In particular for the gauge group SL(2,C) with a plane wave
Hirota ansatz SDYM reduces to a complicated set of algebraic relations due to
de Vega. Here we solve these conditions and the solutions are shown to
correspond to collisions of plane wave kinks. The main result is that for a
class of kinks the resulting phase shifts are non-zero, the solution as a whole
is not pure gauge and so the scattering seems non-trivial. However the stress
energy and Lagrangian density are confined to string like regions in the space
time and in particular are zero for the incoming/outgoing kinks so the solution
does not correspond to physical four point scattering.
| 1991-10-30
| 2009-10-22
|
[
"hep-th"
] |
Andrew Parkes
|
hep-th/9110074
|
A Two Parameter Deformation of the SU(1/1) Superalgebra and the XY
Quantum Chain in a Magnetic Field
|
We show that the XY quantum chain in a magnetic field is invariant under a
two parameter deformation of the SU(1/1) superalgebra. One is led to an
extension of the braid group and the Hecke algebra which reduce to the known
ones when the two parameter coincide. The physical significance of the two
parameters is discussed.
| 1991-10-30
| 2009-10-22
|
[
"hep-th"
] |
Haye Hinrichsen and Vladimir Rittenberg
|
hep-th/9110071
|
Extra Observables in Gauged WZW Models
|
It is known that Liouville theory can be represented as an SL(2,R) gauged WZW
model. We study a two dimensional field theory which can be obtained by
analytically continuing some of the variables in the SL(2,R) gauged WZW model.
We can derive Liouville theory from the analytically continued model, ( which
is a gauged SL(2,C)/SU(2) model, ) in a similar but more rigorous way than from
the original gauged WZW model. We investigate the observables of this gauged
SL(2,C)/SU(2) model. We find infinitely many extra observables which can not be
identified with operators in Liouville theory. We concentrate on observables
which are $(1,1)$ forms and the correlators of their integrals over two
dimensional spacetime. At a special value of the coupling constant of our
model, the correlators of these integrals on the sphere coincide with the
results from matrix models.
| 1991-10-30
| 2009-10-22
|
[
"hep-th"
] |
Nobuyuki Ishibashi
|
hep-th/9110069
|
Analysis of Observables in Chern-Simons Perturbation Theory
|
Chern-Simons Theory with gauge group $SU(N)$ is analyzed from a perturbation
theory point of view. The vacuum expectation value of the unknot is computed up
to order $g^6$ and it is shown that agreement with the exact result by Witten
implies no quantum correction at two loops for the two-point function. In
addition, it is shown from a perturbation theory point of view that the framing
dependence of the vacuum expectation value of an arbitrary knot factorizes in
the form predicted by Witten.
| 1991-10-29
| 2009-10-22
|
[
"hep-th"
] |
M. Alvarez and J.M.F. Labastida
|
hep-th/9110070
|
Heterotic instantons and solitons in anomaly-free supergravity
|
We extend the classical heterotic instanton solutions to all orders in
$\alpha'$ using the equations of anomaly-free supergravity, and discuss the
relation between these equations and the string theory $\beta$-functions.
| 1991-10-29
| 2009-10-22
|
[
"hep-th"
] |
I. Pesando and A. Tollsten
|
hep-th/9110068
|
Two-Dimensional Quantum Gravity on a Disk
|
We study a two-dimensional conformal field theory coupled to quantum gravity
on a disk. Using the continuum Liouville field approach, we compute three-point
correlation functions of boundary operators. The structure of momentum
singularities is different from that of correlation functions on a sphere and
is more complicated. We also compute four-point functions of boundary operators
and three-point functions of two boundary operators and one bulk operator.
| 1991-10-28
| 2009-10-22
|
[
"hep-th"
] |
Yoshiaki Tanii and Shun-ichi Yamaguchi
|
hep-th/9110066
|
Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the
$p$-Adics-Quantum Group Connection
|
We establish a previously conjectured connection between $p$-adics and
quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra
and its generalizations, the conceptual basis for the Macdonald polynomials,
which ``interpolate'' between the zonal spherical functions of related real and
$p$\--adic symmetric spaces. The elliptic quantum algebras underlie the
$Z_n$\--Baxter models. We show that in the $n \air \infty$ limit, the Jost
function for the scattering of {\em first} level excitations in the
$Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function
constructed from the Macdonald polynomials associated to the root system $A_1$.
The partition function of the $Z_2$\--Baxter model itself is also expressed in
terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less
simple way. We relate the two parameters $q$ and $t$ of the Macdonald
polynomials to the anisotropy and modular parameters of the Baxter model. In
particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond
to a discrete sequence of XXZ models. We also discuss the possibility of
``$q$\--deforming'' Euler products.
| 1991-10-24
| 2009-10-22
|
[
"hep-th",
"math.QA"
] |
Peter G. O. Freund and Anton V. Zabrodin
|
hep-th/9110067
|
Some Exact Solutions of String Theory in Four and Five Dimensions
|
We find several classes of exact classical solutions of critical bosonic
string theory, constructed as twisted products of one Euclidean and one
Minkowskian 2D black hole coset. One class of these solutions leads (after
tensoring with free scalars and supersymmetrizing) to a rotating version of the
recently discovered exact black fivebrane. Another class represents a
one-parameter family of axisymmetric stationary four-dimensional targets with
horizons. Global properties and target duality of the 4D solutions are briefly
analyzed.
| 1991-10-24
| 2009-10-22
|
[
"hep-th"
] |
Petr Horava
|
hep-th/9110065
|
An Equivalence Between Momentum and Charge in String Theory
|
It is shown that for a translationally invariant solution to string theory,
spacetime duality interchanges the momentum in the symmetry direction and the
axion charge per unit length. As one application, we show explicitly that
charged black strings are equivalent to boosted (uncharged) black strings. The
extremal black strings (which correspond to the field outside of a fundamental
macroscopic string) are equivalent to plane fronted waves describing strings
moving at the speed of light.
| 1991-10-23
| 2009-10-22
|
[
"hep-th"
] |
James H. Horne, Gary T. Horowitz, and Alan R. Steif
|
hep-th/9110063
|
Fusion Potentials for G_k and Handle Squashing
|
Using Chern-Simons gauge theory, we show that the fusion ring of the
conformal field theory G_k is isomorphic to P(u)/(\del V), where V is a
polynomial in u and (\del V) is the ideal generated by the conditions \del V=0.
We also derive a residue-like formula for the correlation functions in the
Chern-Simons theory thus providing a RCFT version of the residue formula for
the TLG models. An operator that acts like the measure in the residue formula
has the ionterpretation of a handle squashing operator and an explicit formula
for this operator is given.
| 1991-10-22
| 2009-10-22
|
[
"hep-th"
] |
Michael Crescimanno
|
hep-th/9110064
|
New Integrable Systems from Unitary Matrix Models
|
We show that the one dimensional unitary matrix model with potential of the
form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the
eigenvalues, we establish the integrability of a system of particles in one
space dimension in an external potential of the form $a \cos (x+\alpha ) + b
\cos ( 2x +\beta )$ and interacting through two-body potentials of the inverse
sine square type. This system constitutes a generalization of the Sutherland
model in the presence of external potentials. The positive-definite matrix
model, obtained by analytic continuation, is also integrable, which leads to
the integrability of a system of particles in hyperbolic potentials interacting
through two-body potentials of the inverse hypebolic sine square type.
| 1991-10-22
| 2009-10-22
|
[
"hep-th"
] |
Alexios P. Polychronakos
|
hep-th/9110057
|
3-dimensional Gravity from the Turaev-Viro Invariant
|
We study the $q$-deformed su(2) spin network as a 3-dimensional quantum
gravity model. We show that in the semiclassical continuum limit the
Turaev-Viro invariant obtained recently defines naturally regularized
path-integral $\grave{\rm a}$ la Ponzano-Regge, In which a contribution from
the cosmological term is effectively included. The regularization dependent
cosmological constant is found to be ${4\pi^2\over k^2} +O(k^{-4})$, where
$q^{2k}=1$. We also discuss the relation to the Euclidean Chern-Simons-Witten
gravity in 3-dimension.
| 1991-10-21
| 2010-11-01
|
[
"hep-th"
] |
Shun'ya Mizoguchi and Tsukasa Tada
|
hep-th/9110060
|
Complete structure of Z_n Yukawa couplings
|
We give the complete twisted Yukawa couplings for all the Z_n orbifold
constructions in the most general case, i.e. when orbifold deformations are
considered. This includes a certain number of tasks. Namely, determination of
the allowed couplings, calculation of the explicit dependence of the Yukawa
couplings values on the moduli expectation values (i.e. the parameters
determining the size and shape of the compactified space), etc. The final
expressions are completely explicit, which allows a counting of the DIFFERENT
Yukawa couplings for each orbifold (with and without deformations). This
knowledge is crucial to determine the phenomenological viability of the
different schemes, since it is directly related to the fermion mass hierarchy.
Other facts concerning the phenomenological profile of Z_n orbifolds are also
discussed, e.g. the existence of non--diagonal entries in the fermion mass
matrices, which is related to a non--trivial structure of the
Kobayashi--Maskawa matrix. Finally some theoretical results are given, e.g. the
no--participation of (1,2) moduli in twisted Yukawa couplings. Likewise, (1,1)
moduli associated with fixed tori which are involved in the Yukawa coupling, do
not affect the value of the coupling.
| 1991-10-21
| 2015-06-26
|
[
"hep-th"
] |
J.A. Casas, F. Gomez and C. Mu\~noz
|
hep-th/9110059
|
On the Covariant Quantization of the 2nd-Ilk Superparticle
|
This paper is devoted to the quantization of the second-ilk superparticle
using the Batalin-Vilkovisky method. We show the full structure of the master
action. By imposing gauge conditions on the gauge fields rather than on
coordinates we find a gauge-fixed quantum action which is free. The structure
of the BRST charge is exhibited and the BRST cohomology yields the same
physical spectrum as the light- cone quantization of the usual superparticle.
| 1991-10-21
| 2015-06-26
|
[
"hep-th"
] |
J.L. Vazquez-Bello
|
hep-th/9110061
|
Generalised Abelian Chern-Simons Theories and their Connection to
Conformal Field Theories
|
We discuss the generalization of Abelian Chern-Simons theories when $\theta
$-angles and magnetic monopoles are included. We map sectors of two dimensional
Conformal Field Theories into these three dimensional theories.
| 1991-10-21
| 2015-06-26
|
[
"hep-th"
] |
Marco A. C. Kneipp
|
hep-th/9110062
|
Semirigid Geometry
|
We provide an intrinsic description of $N$-super \RS s and $TN$-\SR\
surfaces. Semirigid surfaces occur naturally in the description of topological
gravity as well as topological supergravity. We show that such surfaces are
obtained by an integrable reduction of the structure group of a complex
supermanifold. We also discuss the \s moduli spaces of $TN$-\SR\ surfaces and
their relation to the moduli spaces of $N$-\s\ \RS s.
| 1991-10-21
| 2015-06-26
|
[
"hep-th"
] |
Govindarajan, Nelson, Wong
|
hep-th/9110058
|
Root Systems and Purely Elastic S-Matrices II
|
Starting from a recently-proposed general formula, various properties of the
ADE series of purely elastic S-matrices are rederived in a universal way. In
particular, the relationship between the pole structure and the bootstrap
equations is shown to follow from properties of root systems. The discussion
leads to a formula for the signs of the three-point couplings in the
simply-laced affine Toda theories, and a simple proof of a result due to
Klassen and Melzer of relevance to Thermodynamic Bethe Ansatz calculations.
| 1991-10-21
| 2010-11-01
|
[
"hep-th"
] |
Patrick Dorey
|
hep-th/9110056
|
Chern-Simons Perturbation Theory
|
We study the perturbation theory for three dimensional Chern--Simons quantum
field theory on a general compact three manifold without boundary. We show that
after a simple change of variables, the action obtained by BRS gauge fixing in
the Lorentz gauge has a superspace formulation. The basic properties of the
propagator and the Feynman rules are written in a precise manner in the
language of differential forms. Using the explicit description of the
propagator singularities, we prove that the theory is finite. Finally the
anomalous metric dependence of the $2$-loop partition function on the
Riemannian metric (which was introduced to define the gauge fixing) can be
cancelled by a local counterterm as in the $1$-loop case. In fact, the
counterterm is equal to the Chern--Simons action of the metric connection,
normalized precisely as one would expect based on the framing dependence of
Witten's exact solution.
| 1991-10-20
| 2008-02-03
|
[
"hep-th",
"math.DG",
"math.QA"
] |
Scott Axelrod and I. M. Singer
|
hep-th/9110055
|
Topological Matter, Integrable Models and Fusion Rings
|
We show how topological $G_k/G_k$ models can be embedded into the topological
matter models that are obtained by perturbing the twisted $N=2$ supersymmetric,
hermitian symmetric, coset models. In particular, this leads to an embedding of
the fusion ring of $G$ as a sub-ring of the perturbed, chiral primary ring. The
perturbation of the twisted $N=2$ model that leads to the fusion ring is also
shown to lead to an integrable $N=2$ supersymmetric field theory when the
untwisted $N=2$ superconformal field theory is perturbed by the same operator
and its hermitian conjugate.
| 1991-10-19
| 2009-10-22
|
[
"hep-th"
] |
D. Nemeschansky and N.P. Warner
|
hep-th/9110053
|
Duality, Quotients, and Currents
|
We study the generalization of $R\to 1/R$ duality to arbitrary conformally
invariant sigma models with an isometry. We show that any pair of dual sigma
models can be represented as quotients of a self-dual sigma model obtained by
gauging different combinations of chiral currents. This observation is used to
clarify the interpretation of the generalized duality as a symmetry of
conformal field theory. We extend these results to $N=2$ supersymmetric sigma
models.
| 1991-10-18
| 2009-10-22
|
[
"hep-th"
] |
Martin Rocek and Erik Verlinde
|
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