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
Loop Groups
Vertex Operator Algebra
Witt Algebra and Virasoro Algebra
Unitary Highest Weight Representations
The Verma Module
The Fock Space
The Integrability Theorem
The Semigroup of Annuli
Conformal Welding Problem
The Symplectic Hilbert Space
Embed Into The Semigroups