arXiv 1111.20252011-11-08hep-th

超对称黑洞的量子熵

Quantum entropy of supersymmetric black holes

Joao Gomes

备注：: arXiv admin note: substantial text overlap with arXiv:1111.1161, arXiv:1012.0265

摘要：

本文从微观和宏观两个方面综述了弦论中关于一大类超对称黑洞量子熵的研究进展。在微观场论方面，我们提出了新的结果有关计数的黑洞微观状态的电荷矢量与非平凡的算术对偶不变量。在宏观引力方面，我们提出了一个新的应用本地化技术的超引力泛函积分计算这些黑洞的量子熵。局域化导致一个巨大的简化的路径积分的弦论在AdS_2通过减少到一个有限维积分。局部化解用n_v+1个参数表示，其中n_v为N=2超引力理论中的矢量多重态个数。作为一个例子，我们表明，对于四维大黑洞，保持四个超对称的环面紧化IIB弦论，宏观简并精确地同意在一个精确的Rademacher展开的微观答案，除了Kloosterman总和，在原则上可以计算的所有条款。推广以前的工作，这些有限的电荷贡献的领先贝肯斯坦-霍金熵也可以被看作是一个例子的“精确全息”的上下文中的AdS_2/CFT_1对应。

英文摘要：

We review recent progress concerning the quantum entropy of a large class of supersymmetric black holes in string theory both from the microscopic and macroscopic sides. On the microscopic field theory side, we present new results concerning the counting of black hole microstates for charge vectors with nontrivial arithmetic duality invariants. On the macroscopic gravitational side, we present a novel application of localization techniques to a supergravity functional integral to compute the quantum entropy of these black holes. Localization leads to an enormous simplification of a path integral of string theory in AdS_2 by reducing it to a finite dimensional integral. The localizing solutions are labeled by n_v+1 parameters, with n_v the number of vector multiplets in the theory of N=2 supergravity. As an example we show, for four dimensional large black holes which preserve four supersymmetries in toroidally compactified IIB string theory, that the macroscopic degeneracy precisely agrees with all the terms in an exact Rademacher expansion of the microscopic answer except for Kloosterman sums which in principle can be computed. Generalizing previous work, these finite charge contributions to the leading Bekenstein-Hawking entropy can also be viewed as an instance of "exact holography" in the context of AdS_2/CFT_1 correspondence.

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英文摘要：

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