Lectures on Conformal Field Theory

TL;DR

This paper provides an accessible introduction to conformal field theories across dimensions, covering foundational concepts, the conformal bootstrap, boundary theories, and applications to AdS/CFT, aimed at graduate students and a broader audience.

Contribution

It offers a comprehensive overview of conformal field theory topics, including recent developments like the bootstrap program and boundary theories, tailored for learners with basic quantum mechanics and quantum field theory knowledge.

Findings

Introduces conformal field theory concepts and methods.

Summarizes the conformal bootstrap approach.

Discusses applications to AdS/CFT correspondence.

Abstract

These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions, with applications related to topics of particular interest: topics include the conformal bootstrap program, boundary conformal field theory, and applications related to the AdS/CFT correspondence. We assume the reader to be familiar with quantum mechanics at the graduate level and to have some basic knowledge of quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help.