Statistical Field Theories

Recent developments in theoretical physics include new instances of the unification of quite different phenomena. The theoretical community is challenged by the growing interactions between high-energy physics, statistical physics, and condensed matter physics. The common language, though, is exact solutions of two-dimensional and conformable field theories. This volume is a faithful representation of this interdisciplinary domain. Conformable and integrable field theories have been active research topics for several decades. The main recent developments concern the boundary effects and applications to disordered systems. The number of applications of the exact methods to condensed-matter problems has been growing over the years. Nowadays it is widely recognized that strongly interacting systems in low dimensions can be successfully described by integrable and conformable theories. This volume is an indispensable aid to those seeking to find their way in this domain.

Preface

ix

Part I INTEGRABLE MODELS AND CONFORMAL FIELD THEORIES

Field Theory of Scaling Lattice Models: The Potts Antiferromagnet

3

(10)

Gesualdo Delfino

The ODE/IM Correspondence and PT-symmetric Quantum Mechanics

13

(12)

Patrick Dorey

Clare Dunning

Roberto Tateo

Coupled Models W D(p)3: Their Fixed Points

25

(8)

Vladimir S. Dotsenko

Xuan Son Nguyen

Raoul Santachiara

The Combinatorics of Alternating Tangles: From Theory to Computerized Enumeration

33

(14)

Jesper Lykke Jacobsen

Paul Zinn-Justin

On the Sine-Gordon One-Point Functions

47

(10)

Rubik H. Poghossian

On Vertex Operators and the Normalization of Form Factors

57

(10)

Yaroslav Pugai

Integrable Chain Models with Staggered R-matrices

67

(12)

Ara G. Sedrakyan

On the Quantization of Affine Jacobi Varieties of Spectral Curves

79

(12)

Fedor A. Smirnov

Vadim Zeitlin

Rational Conformal Field Theory in Four Dimensions

91

(14)

Nikolay M. Nikolov

Yassen S. Stanev

Ivan T. Todorov

Perturbed Conformal Field Theory on a Sphere

105

(14)

Alexei B. Zamolodchikov

Part II INTEGRABLE AND CONFORMAL FIELD THEORIES WITH BOUDARIES

Two-boundary Integrability and the Josephson Current in a Luttinger Liquid

119

(10)

Jean-Szebastien Caux

Hubert Saleur

Francesco Siano

Coupling the Sine-Gordon Field Theory to a Mechanical System at the Boundary

129

(10)

Pascal Baseilhac

Gustav W. Delius

Alan George

Reflection Amplitudes and Expectation Values of Fields in Integrable Boundary Theories

139

(14)

Vladimir A. Fateev

Integrable Boundary Conditions for the O(N) Nonlinear Sigma Model

153

(8)

Marco Moriconi

Verlinde Nim-reps for Charge Conjugate sl(N) WZW Theory

161

(10)

Valentina B. Petkova

Jean-Bernard Zuber

Open-String Models with Broken Supersymmetry

171

(14)

Augusto Sagnotti

Conformal Boundary Conditions and 3D Topological Field Theory

185

(10)

Jurgen Fuchs

Ingo Runkel

Christoph Schweigert

The Spectrum of Boundary Sine-Gordon Theory

195

(12)

Zoltan Bajnok

Laszlo Palla

Gabor Takacs

Part III DISORDERED SYSTEMS

A Classification of Non-Hermitian Random Matrices

207

(8)

Denis Bernard

Andre LeClair

The Stress Tensor in Quenched Random Systems

215

(8)

John Cardy

Taking N → 0 with S Matrices

223

(16)

Paul Fendley

Scattering in Quantum Field Theories with Supergroup Invariance

239

(12)

Hubert Saleur

Birgit Wehefritz-Kaufmann

Nishimori Point in Random-Bond Ising and Potts Models in 2D

251

(12)

Andreas Honecker

Jesper L. Jacobsen

Marco Picco

Pierre Pujol

2D Random Dirac Ferminos: Large N Approach

263

(16)

Didina Serban

Part IV QUANTUM HALL EFFECT AND CONDENSED MATTER APPLICATIONS

Impurities in One Dimension

279

(10)

Sebastian Eggert

Axions, Quantum Mechanical Pumping, and Primeval Magnetic Fields

289

(16)

Jurg Frohlich

Bill Pedrini

Paired and Clustered Quantum Hall States

305

(12)

Kareljan Schoutens

Eddy Ardonne

Frank J.M. van Lankvelt

Integrability and Conformal Symmetry in the BCS Model

317

(12)

German Sierra

Wavefunction Statistics at the Quantum Hall Critical Point

329

(8)

Alexei M. Tsvelik

Aharonov-Bohm Effect in the Quantum Hall Regime and Laplacian Growth Problems

337

(14)

Paul B. Wiegmann

Index

351

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