标题： 量子黑洞：超对称性和精确结果 显示英文标题

标题： Quantum black holes: supersymmetry and exact results

摘要： 将黑洞熵解释为统计熵是弦理论的一大成功。 在本文中，我们回顾了这一主题的最新进展，重点在于理解黑洞熵的量子效应。 超对称在这些发展中起着关键作用，并导致了原型系统，使我们能够非常精确地讨论量子效应。 我们的讨论有两个方面，都涉及计算超对称指标的引力路径积分。 在第一个方面，我们讨论微正则系综中的超对称黑洞，它们与环境分离，可以作为独立的量子系统来处理。 使用超对称局部化的方法，可以仅用引力变量纯粹地得出这类系统的整数量子简并度。 在第二个方面，我们考虑引力中的大正则系综，在这种情况下，黑洞作为渐近平坦或反德西特空间中具有有限作用量的激发态出现。 在此背景下，我们讨论引力指标的鞍点，以及它们如何在半经典近似下的领先阶之外，再现与全息超对称场理论指标一致的黑洞作用量和熵。 最后，我们讨论引力指标如何告知我们关于鞍点非微扰求和的详细结构以及理论产生的相。 在整个过程中，我们试图突出超重力的方法和基础概念在推动这些发展中的核心作用。 显示英文摘要

摘要： The explanation of black hole entropy as statistical entropy is one of the big successes of string theory. In this article we review recent progress in this subject, focussing on understanding quantum effects on black hole entropy. Supersymmetry plays a key role in these developments and leads to prototype systems where we can discuss quantum effects to great precision. Our discussion has two strands, both of which involve the gravitational path integral that calculates the supersymmetric index. In the first strand we discuss supersymmetric black holes in the microcanonical ensemble, which are decoupled from the environment and can be treated as independent quantum systems. Using methods of supersymmetric localization one can arrive at the integer quantum degeneracies of such systems purely in terms of the gravitational variables. In the second strand we consider grand-canonical ensembles in gravity in which black holes arise as a finite-action excitation in asymptotically flat or Anti de Sitter space. In this context we discuss the saddle-points of the gravitational index, and how they reproduce the black hole action and entropy that agree with the index of the holographic superconformal field theory even beyond the leading order in the semiclassical approximation. Finally we discuss how the gravitational index informs us about the detailed structure of the non-perturbative sum over saddle points and the resulting phases of the theory. Throughout, we try to highlight the central role played by the methods as well as foundational concepts of supergravity in driving these developments.