id
large_stringlengths
9
16
title
large_stringlengths
1
382
abstract
large_stringlengths
3
6.09k
publish_date
date32
update_date
date32
categories
large listlengths
1
13
authors
large_stringlengths
3
62.8k
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 They are intentionally 1.5 years out of date. 0.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 postscript file was submitted separately in uuencoded tar-compressed format.
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