Introduction

Conformal field theory is a quantum field theory invariant under conformal (angle-preserving) transformations, which powerfully constrains correlation functions and often makes theories exactly solvable, especially in two dimensions. It underpins string worldsheet dynamics and captures universality classes at critical points in statistical and condensed matter systems.

Contents

Virasoro Algebra

Witt Algebra and Virasoro Algebra
Unitary Highest Weight Representations
The Verma Module
The Integrability Theorem
Loop Groups
Vertex Operator Algebra

The Semigroup of Annuli

The Semigroup of Annuli
Conformal Welding Problem

The Fock Model

The Fock Space
Symplectic Hilbert Spaces
The Weil Representation
Embed Into The Semigroups