TASI Lectures: Introduction to the AdS/CFT Correspondence

TL;DR

This paper provides an introductory review of the AdS/CFT correspondence, explaining how certain string backgrounds are dual to conformal gauge theories, and discusses specific examples including the ${ m AdS}_5 imes X_5$ backgrounds and their dual field theories.

Contribution

It introduces the foundational ideas of AdS/CFT, illustrating the duality between supergravity solutions and conformal gauge theories with explicit examples.

Findings

Duality between D3-branes and supergravity backgrounds.

Correlation functions determined by supergravity boundary conditions.

Examples include ${ m AdS}_5 imes S^5$ and ${ m AdS}_5 imes T^{1,1}$ backgrounds.

Abstract

This is an introductory review of the AdS/CFT correspondence and of the ideas that led to its formulation. We show how comparison of stacks of D3-branes with corresponding supergravity solutions leads to dualities between conformal large $N$ gauge theories in 4 dimensions and string backgrounds of the form $AdS_5\times X_5$ where $X_5$ is an Einstein manifold. The gauge invariant chiral operators of the field theory are in one-to-one correspondence with the supergravity modes, and their correlation functions at strong `t Hooft coupling are determined by the dependence of the supergravity action on AdS boundary conditions. The simplest case is when $X_5$ is a 5-sphere and the dual gauge theory is the ${\cal N}=4$ supersymmetric SU(N) Yang-Mills theory. We also discuss D3-branes on the conifold corresponding to $X_5$ being a coset space $T^{1,1}=(SU(2)\times SU(2))/U(1)$. This background is dual to a certain ${\cal N}=1$ superconformal field theory with gauge group $SU(N)\times SU(N)$.