Conformal Field Theory and Solvable Lattice Models

M Jimbo

• Publisher: Academic Press
• Year: 2012
• Print ISBN:
  9780123853400
• eBook ISBN:
  9780323150354
• Topic: Physical Sciences
• Subtopic: Energy

Advanced Studies in Pure Mathematics, 16: Conformal Field Theory and Solvable Lattice Models contains nine papers based on the symposium "Conformal field theory and solvable lattice models" held at RIMS, Kyoto, May 1986. These papers cover the following active areas in mathematical physics: conformal field theory, solvable lattice models, affine and Virasoro algebra, and KP equations. The volume begins with an analysis of 1 and 2 point correlation functions of the Gibbs measure of random matrices. This is followed by separate chapters on solvable solid-on-solid (SOS) models; lectures on conformal field theory; the construction of Fermion variables for the 3D Ising Model; and vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. Subsequent chapters deal with Hecke algebra representations of braid groups and classical Yang-Baxter equations; the relationship between the conformal field theories and the soliton equations (KdV, MKdV and Sine-Gordon, etc.) at both quantum and classical levels; and a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy.

Table of contents

• Front Cover
• Conformal Field Theory and Solvable Lattice Models
• Copyright Page
• Table of Contents
• Foreword
• Preface
• Chapter 1. Scaling Limit Formula for 2-Point Correlation Function of Random Matrices
• Chapter 2. Exactly Solvable SOS Models II: Proof of the star-triangle relation and combinatorial identities
• Chapter 3. Lectures on Conformal Field Theory
• Chapter 4. Fermion Representations for the 2D and 3D Ising Models
• Chapter 5. Null Field Construction in Conformal and Superconformal Algebras
• Chapter 6. Hecke Algebra Representations of Braid Groups and Classical Yang-Baxter Equations
• Chapter 7. Virasoro Algebra, Vertex Operators, Quantum Sine-Gordon and Solvable Quantum Field Theories
• Chapter 8. Vertex Operators in Conformal Field Theory on P1 and Monodromy Representations of Braid Group
• Chapter 9. Supersymmetric Extension of the Kadomtsev-Petviashvili Hierarchy and the Universal Super Grassmann Manifold