Anti-de Sitter space, thermal phase transition, and confinement in gauge theories

Edward Witten

Research output: Contribution to journalArticlepeer-review

2740 Scopus citations

Abstract

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of 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.

Original languageEnglish (US)
Pages (from-to)505-532
Number of pages28
JournalAdvances in Theoretical and Mathematical Physics
Volume2
Issue number3
DOIs
StatePublished - May 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

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