A guide to two-dimensional conformal field theory

TL;DR

This paper provides a comprehensive and accessible review of two-dimensional conformal field theory, covering foundational formalism, advanced topics, and connections to integrable models and mathematical structures.

Contribution

It offers an elementary, flexible exposition of the basic formalism and introduces advanced topics like higher genus surfaces and isomonodromic deformations.

Findings

Clarifies the formalism of 2D conformal field theory

Explores connections to integrable models and mathematical structures

Provides guidance to further literature on advanced topics

Abstract

This is a review of two-dimensional conformal field theory including some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is as elementary and flexible as possible at the same time. Some advanced topics like conformal field theory on higher genus surfaces and relations to the isomonodromic deformation problem are discussed, for other topics we offer a first guide to the literature.