Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories

Details Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories

1998-03-16

arxiv.org/abs/hep-th/9803131v2

Adv.Theor.Math.Phys.2:505-532,1998

Physics

High Energy Physics

High Energy Physics - Theory

28 pp., added references and minor corrections

Scientific paper

The correspondence between supergravity (and string theory) on $AdS$ space and boundary conformal field theory relates the thermodynamics of ${\cal N}=4$ super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large $AdS$ Schwarzschild black hole must scale ``holographically'' with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large $N$ gauge theories in four dimensions without supersymmetry.

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