This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a well-posed road from simple lattice models to CFTs.
Structured in two parts, the book begins by exploring several two-dimensional lattice models, their phase transitions, and their conjectural connection with CFT. Through these lattice models and their local fields, the fundamental ideas and results of two-dimensional CFTs emerge, with a special emphasis on the Unitary Minimal Models of CFT. Delving into the delicate ideas that lead to the classification of these CFTs, the authors discuss the assumptions on the lattice models whose scaling limits are described by CFTs. This produces a probabilistic rather than an axiomatic or algebraic definition of CFTs.
Suitable for graduate students and researchers in mathematics and physics, Lattice Models and Conformal Field Theory introduces the ideas at the core of Statistical Field Theory. Assuming only undergraduate probability and complex analysis, the authors carefully motivate every argument and assumption made. Concrete examples and exercises allow readers to check their progress throughout.
Introduction
Lattice models, phase transitions, and critical exponents
Statistical and quantum field theories
Conformal field theory
Conformal field theory: Minimal models on the plane
Local fields and correlations
Stress-energy tensor and conformal Ward identities
Unitarity and radial quantization
Primary fields and conformal families
Unitary minimal models, lattice models, and loop models
Bibliography
Index
Franck Gabriel, Universite Lyon 1, France, Clement Hongler, EPFL, Lausanne, Switzerland, and Francesco Spadaro, Zurich, Switzerland.
