TASI Lectures: Introduction to the AdS/CFT Correspondence

TL;DR

The paper surveys the AdS/CFT correspondence, showing how stacks of D3-branes yield dual descriptions as string theory on $AdS_5\times X_5$ for Einstein manifolds $X_5$, with operator–field mapping that allows computation of strong-coupling correlators from gravity. It connects D-brane thermodynamics and black-hole entropy to large-N gauge theory thermodynamics, and demonstrates exact matches between supergravity absorption cross-sections and D-brane calculations, underpinning the GKPW holographic dictionary. Beyond the canonical $AdS_5\times S^5$ dual to ${\cal N}=4$ SYM, it extends to ${\cal N}=1$ theories via $AdS_5\times T^{1,1}$ and analyzes chiral operators, dibaryons, and wrapped branes, illustrating rich operator spectra and nontrivial IR dynamics such as Seiberg duality cascades and confinement in gravity duals.

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 $SU(N)\times SU(N)$.