Quantum field theory, statistical mechanics, quantum groups and topology : proceedings of the NATO advanced research workshop, University of Miami, 7-12 January 1991

366 Pages·1992·20.076 MB·English

by  Curtright, Thomas, Mezincescu, Luca, Nepomechie, Rafael I.

Quantum Field Theory, Statistical Mechanics,
Quantum Groups, and Topology
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Proceedings of the NATO Advanced Research Workshop
QUANTUM FIELD THEORY,
STATISTICAL MECHANICS,
QUANTUM GROUPS AND
TOPOLOGY
University of Miami 7 - 12 January 1991
edited by
Thomas Curtright, Luea Mezincescu &.. Rafael Nepomechie
Department of Physics, University of Miami
.~ World Scientific
... Singapore· New Jersey· London· Hong Kong
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QUAN'Il1M nELD THEORY. Sl'A11S11CAL MECHANICS,
QUANnIM GRoups, AND TOPOLOOY
Copyriahl e 1992 by World Scieillific PublWUlI1 Co. Pte. LId.
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ISBN 9789814537605
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v
CONTENTS
Preface ix
Integrability in Random Matrix Models 1
L. Alvarez-Gaume
On Looking for Solutions of the Star-triangle Relations 11
R. J. Baxter
Casimir Effect in Conformal Theories in Higher Dimensions 17
John L. Cardy
Quantum Cosmology on the Worldsheet 26
A. R. Cooper, L. Susskind, and L. Thorlacius
A Note on the Branching Rule for Cyclic Representations of Uq{gln) 46
Etsuro Date, Michio Jimbo, and Kei Miki
Exact S-matrices for Toda Theories based on Lie Superalgebras 55
G. W. Delius, M. T. Grisaru, S. Penati, and D. Zanon
Superconformal Algebras as Hidden Symmetries in Topological
Conformal Field Theories 68
Tohru Eguchi, Shinobu Hosono, and Sung-kil Yang
Quantized Planes and Multiparameter Deformations of Heisenberg
and GL{N) Algebras 81
D. B. Fairlie and Cosmas Zachos
p-Adics and q-Deformations 93
Peter G. O. Freund
The Quantum Group Structure of 2D Gravity 97
Jean-Loup GenJais
A Note on Liouville Theory and the Uniformization of Riemann
Surfaces 115
Cesar Gomez and German Sierra
vi
Gauss Codes and Quantum Groups 123
Louis H. Kauffman
Finite-size Effects as a Probe of Non-perturbative Physics:
Perturbed CFTs, Factorizable Scattering, the Thermodynamic
Bethe Ansatz, and All That 155
Timothy R. Klassen and Ezer Melzer
Differential Equations for Quantum Correlation Functions 175
V. Korepin
Correlation Functions of Sine-Gordon Model at Free Fermion
Point as Fredholm Determinants 176
H. [toyama, V. E. Korepin, and H. B. Thacker
Level Crossing and the Chiral Potts Model 184
Barry M. McCoy
Distinguishable Particles in Delta Interaction 193
J. B. McGuire
Exactly Solved Models with Quantum Algebra Symmetry 200
Luca Mezincescu and Rafael!. Nepomechie
A Quantum Generated Symmetry of Conformal and Topological
Field Theory 218
S. G. Naculich, H. A. Riggs, H. J. Schnitzer,
and E. J. Mlawer
Noncritical Strings Beyond c = 1 233
Joseph Polchinski
Sub critical Strings in 1 < D ~ 25 241
Christian R. Preitschopf and Charles B. Thorn
Recent Results on Two-dimensional Supergravity 255
z. Qiu
Quantum Supergroups 264
N. Reshetikhin
vii
Loop Calculations in BRST Quantized Chiral W3 Gravity 283
K. Schoutens, A. Sevrin, and P. van Nieuwenhuizen
Solvable Lattice Models, Corner Transfer Matrices, and Infinite
Dimensional Lie Algebras 302
H. B. Thacker
Null Strings, Twistors, and Higher-Spin Algebras 313
P. K. Townsend
Integrable Field Theory of Self-avoiding Polymers in 2D 324
A. B. Zamolodchikov
Using Functional Methods to compute Quantum Effects in
the Liouville Model 333
T. Curtright and G. Ghandour
List of Participants 347
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ix
PREFACE
In recent years, much progress has been made on integrable two-dimen
sional systems and conformal field theory, and on related topological quantum
field theories in three dimensions. Quantum groups and knot theory provide
important mathematical links between these subjects. Because of the close
interrelation of all these disciplines, new discoveries in one of them have quickly
led to progress in the others.
This volume contains the proceedings of a NATO Advanced Research
Workshop on these interrelated disciplines. The workshop took place 7-12 Jan
uary 1991 in the new James L. Knight Physics Building at the University of
Miami.
The principal goal of the workshop was to advance the pace of discoveries
in theoretical research on the chosen topics by providing an opportunity for pre
sentations of new results, and by providing a forum to discuss likely directions
for future work. The workshop brought together a unique combination of lead
ing researchers in integrable systems, conformal field theory, quantum groups,
and knot theory, thereby providing an opportunity for a cross-fertilization of
ideas. Hopefully, the experience has led to further progress in all ofthese areas.
A large portion of the workshop dealt with so-called "integrable models."
Such models provide useful paradigms in quantum field theory and statisti
cal mechanics. They serve as foundations for constructing many of the most
important theoretical structures iIi physics, including string theory-the most
acceptable candidate for a unified theory of all interactions which incorporates
the standard model of particle physics.
The proceedings contain a number of new results in two-dimensional
physics. Among the topics that are discussed: integrable lattice models, in
cluding the chiral Potts model and its generalizations; quantum 2D gravity
and Liouville theory, and their relation to string theory; and various aspects
of integrable perturbations of conformal field theories.
We thank all the participants for making the workshop an enjoyable and
informative gathering, and we thank the funding agency, NATO, for providing
a generous and realistic level of financial support. We especially thank Gio
vanni Venturi, former Director of NATO Advanced Research Workshops Pro
gram, for his strong encouragement. Finally, we thank George Alexandrakis,
Chairman of the Department of Physics, and David Wilson, former Dean of
the College of Arts and Sciences, University of Miami, for their enthusiastic
sanctioning of the workshop.
The Editors