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

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.

27 pages, lecture notes from the Cargese 2002 summer school. v2 : references added. v3 : references and clarifications added

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• The Mesonic Branch of the Deformed Conifold
• Two-gluon and trigluon glueballs from dynamical holography QCD
• The decay width of stringy hadrons
• A 1+1 field theory spectrum from M theory
• Towards the QCD String: 2+1 dimensional Yang-Mills theory in the planar limit
• Exotic smooth R^4, geometry of string backgrounds and quantum D-branes