Black Holes in 4D N=4 Super-Yang-Mills Field Theory

被引:148
作者
Benini, Francesco [1 ,2 ,3 ]
Milan, Paolo [1 ,2 ]
机构
[1] SISSA, Via Bonomea 265, I-34136 Trieste, Italy
[2] Ist Nazl Fis Nucl, Sez Trieste, Via Valerio 2, I-34127 Trieste, Italy
[3] Abdus Salaam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy
关键词
Gravitation; Particles and Fields; String Theory; PARTITION-FUNCTIONS; PHASE-TRANSITION; INDEX;
D O I
10.1103/PhysRevX.10.021037
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Black-hole solutions to general relativity carry a thermodynamic entropy, discovered by Bekenstein and Hawking to be proportional to the area of the event horizon, at leading order in the semiclassical expansion. In a theory of quantum gravity, black holes must constitute ensembles of quantum microstates whose large number accounts for the entropy. We study this issue in the context of gravity with a negative cosmological constant. We exploit the most basic example of the holographic description of gravity (AdS/CFT): type IIB string theory on AdS(5) x S-5, equivalent to maximally supersymmetric Yang-Mills theory in four dimensions. We thus resolve a long-standing question: Does the four-dimensional N = 4 SU(N) Super-Yang-Mills theory on S-3 at large N contain enough states to account for the entropy of rotating electrically charged supersymmetric black holes in 5D anti-de Sitter space? Our answer is positive. By reconsidering the large N limit of the superconformal index, using the so-called Bethe-ansatz formulation, we find an exponentially large contribution which exactly reproduces the Bekenstein-Hawking entropy of the black holes. Besides, the large N limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics. Our method opens the way toward a quantitative study of quantum properties of black holes in anti-de Sitter space.
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页数:21
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