Introduction to the Maldacena Conjecture on AdS/CFT

TL;DR

The notes distill the core ideas of AdS/CFT by building from the geometry of AdS spaces to the brane constructions that realize near-horizon AdS factors, and then instantiate the bulk/boundary dictionary via concrete bulk propagators for scalars, gauge fields, and massive modes. They connect the bulk fields to boundary conformal operators, illustrate how boundary correlators are extracted from bulk actions, and discuss how finite-temperature deformations of AdS backgrounds can model confinement and a mass gap in large N QCD-like theories. The work emphasizes that in the large N and large λ limit, classical supergravity computations capture nonperturbative features of the boundary CFT, and that KK reductions on compact spheres encode rich operator multiplets with explicit dimension/representation matches. Together, the lectures outline a concrete, calculationally accessible framework to probe strong coupling physics of gauge theories via holography, and sketch pathways to model real-world QCD-like dynamics within this holographic paradigm.

Abstract

These lectures do not at all provide a general review of this rapidly growing field. Instead a rather detailed account is presented of a number of the most elementary aspects.