Introduction to AdS-CFT

TL;DR

This paper provides a comprehensive introduction to AdS-CFT correspondence, covering foundational concepts, key examples like ${ m extbf{N}}=4$ Super Yang-Mills, and various applications in gauge/gravity duality for graduate students.

Contribution

It offers a self-contained overview of AdS-CFT, integrating field theory, gravity, and string theory concepts, and discusses recent applications and properties of gravity duals.

Findings

Explains the AdS-CFT correspondence and its foundational elements.

Describes applications such as 3-point functions and quark-antiquark potential.

Highlights properties of gravity duals of gauge theories.

Abstract

These lectures present an introduction to AdS-CFT, and are intended both for begining and more advanced graduate students, which are familiar with quantum field theory and have a working knowledge of their basic methods. Familiarity with supersymmetry, general relativity and string theory is helpful, but not necessary, as the course intends to be as self-contained as possible. I will introduce the needed elements of field and gauge theory, general relativity, supersymmetry, supergravity, strings and conformal field theory. Then I describe the basic AdS-CFT scenario, of ${\cal N}=4 $ Super Yang-Mills's relation to string theory in $AdS_5\times S_5$, and applications that can be derived from it: 3-point functions, quark-antiquark potential, finite temperature and scattering processes, the pp wave correspondence and spin chains. I also describe some general properties of gravity duals of gauge theories.