The non-AdS/non-CFT correspondence, or three different paths to QCD

TL;DR

The work surveys non-AdS/non-CFT holographic approaches to QCD-like dynamics, outlining three main routes from the AdS/CFT framework: (i) mass deformations of ${\cal N}=4$ SYM (Polchinski-Strassler), (ii) compactifications leading to 3+1D ${\cal N}=1$ YM via little string theory (Maldacena-Nunez), and (iii) the Klebanov-Strassler dual with a duality cascade. It emphasizes how each path yields qualitatively QCD-like features—mass gaps, confinement, and chiral symmetry breaking—yet faces challenges in achieving quantitative control due to highly curved backgrounds and RR fields. The notes illustrate that a limiting string dual to YM exists in principle, but a practical, fully controlled description remains elusive. Collectively, these constructions map the landscape of holographic QCD models and guide ongoing efforts to refine the strong-coupling, nonperturbative description of YM-like theories.

Abstract

In these lecture notes from the 2002 Cargese summer school we review the progress that has been made towards finding a string theory for QCD (or for pure (super)Yang-Mills theory) following the discovery of the AdS/CFT correspondence. We start with a brief review of the AdS/CFT correspondence and a general discussion of its application to the construction of a string theory for QCD. We then discuss in detail two possible paths towards a QCD string theory, one which uses a mass deformation of the N=4 super Yang-Mills theory (the Polchinski-Strassler background) and the other using a compactification of "little string theory" on a 2-sphere (the Maldacena-Nunez solution). A third approach (the Klebanov-Strassler solution) is described in other lectures of this school. We briefly assess the advantages and disadvantages of all three approaches.