TASI lectures on AdS/CFT

TL;DR

This paper introduces the AdS/CFT correspondence, explaining how boundary operators in AdS relate to conformal field theories, and discusses applications, boundary stress tensors, and Mellin amplitudes in this duality framework.

Contribution

It provides a comprehensive review of AdS/CFT, including boundary operators, stress tensors, and Mellin amplitudes, highlighting their roles in understanding strongly coupled QFTs.

Findings

Boundary operators in fixed AdS resemble CFT operators

Including dynamical metrics yields boundary stress tensors

Mellin amplitudes are useful for CFT correlation functions

Abstract

We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of the main properties of Mellin amplitudes for CFT correlation functions and their uses in the context of AdS/CFT.