Supersymmetric Gauge Theories and the AdS/CFT Correspondence

TL;DR

This paper provides a comprehensive overview of supersymmetric gauge theories, supergravity, and superstring theory, focusing on the AdS/CFT correspondence and its applications to correlation functions and holographic RG flows.

Contribution

It offers a detailed pedagogical explanation of the AdS/CFT correspondence, including its application to N=4 super-Yang-Mills theory and holographic RG flows, with problem sets for learning.

Findings

Correlation functions in N=4 SYM analyzed via AdS/CFT

Holographic RG flows and conformal anomaly discussed

Geometry and symmetries of anti-de Sitter space explained

Abstract

In these lecture notes we first assemble the basic ingredients of supersymmetric gauge theories (particularly N=4 super-Yang-Mills theory), supergravity, and superstring theory. Brane solutions are surveyed. The geometry and symmetries of anti-de Sitter space are discussed. The AdS/CFT correspondence of Maldacena and its application to correlation functions in the the conformal phase of N=4 SYM are explained in considerable detail. A pedagogical treatment of holographic RG flows is given including a review of the conformal anomaly in four-dimensional quantum field theory and its calculation from five-dimensional gravity. Problem sets and exercises await the reader.