Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
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The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of J\f = 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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The large-time decay of the retarded correlators can be understood through complex frequencies, analogous to thermal quasinormal modes.
“Since tt > 0 in our Green's functions, they are actually retarded correlators, and the large-time decay can be understood in terms of complex frequencies, a thermal analog of the so-called “quasinormal modes” [9].”
From Very long time scales and black hole thermal equilibrium (2003) · cites this paper as [9]
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- Authors
- Witten, E.
- Affiliations
- Princeton University (US)
- Corresponding author
- Witten, Edward
- ORCID
- Witten, Edward
- Venue
- Advances in Theoretical and Mathematical Physics
- Publisher
- International Press of Boston
- Published
- 1998
- Volume
- 2
- Issue
- 3
- Pages
- 505-532
- ISSN
- 1095-0753 (ISSN-L)
- 1095-0761
- OpenAlex
- W2129925474
- Cited by
- 3,915
- References
- 83
- Citations by year
- 2026: 114 · 2025: 156 · 2024: 198 · 2023: 153 · 2022: 150 · 2021: 159 · 2020: 193 · 2019: 126 · 2018: 130 · 2017: 136 · 2016: 182 · 2015: 162 · 2014: 137 · 2013: 154 · 2012: 155
- FWCI
- 70.73
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Advances in Theoretical and Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- AdS/CFT correspondence, anti-de Sitter space, Schwarzschild black hole, temperature-induced phase transition, center symmetry breaking, magnetic confinement, mass gap, holographic entropy, large N gauge theory, supersymmetric Yang-Mills theory, supergravity, string theory
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