Anti-de Sitter space, thermal phase transition, and confinement in gauge theories. (English) Zbl 1057.81550

Summary: The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of \({\mathcal N}=4\) 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.


81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
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