Lectures On AdS-CFT At Weak 't Hooft Coupling At Finite Temperature

Abstract

This is an introductory lecture note aiming at providing an overview of the AdS-CFT correspondence at weak 't Hooft coupling at finite temperature. The first aim of this note is to describe the equivalence of three interesting thermodynamical phenomena in theoretical physics, namely, Hawking-Page transition to black hole geometry, deconfinement transition in gauge theories, and vortex condensation on string worldsheets. The Hawking-Page transition and the deconfinement transition in weakly coupled gauge theories are briefly reviewed. Emphasis is on the study of 't Hooft-Feynman diagrams in the large $N$ gauge theories, which are supposed to describe closed string worldsheets and probe the above equivalence. Nature of the 't Hooft-Feynman diagrams at finite temperature is analyzed, both in the Euclidean signature (the imaginary time formalism) and in the Lorentzian signature (the real time formalism). The second aim of this note is to give an introduction to the real time formalism applied to AdS-CFT.

Based on lectures delivered at IPM String School and Workshop April 2006, Strings 2006 Shanghai Workshop and Hangzhou Workshop June, ICTS-USTC March 2006 and Chulalongkorn University April 2006. 50 pages, 18 figures; v2 minor corrections

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• Matching the Hagedorn temperature in AdS/CFT
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