标题： 近极端黑洞的熵与谱：非微扰问题的经典膜解 显示英文标题

标题： Entropy and Spectrum of Near-Extremal Black Holes: semiclassical brane solutions to non-perturbative problems

摘要： 黑洞熵在极端情况下已被观察到在指数级低温 $T\sim e^{-S_0}$ 下普遍变为负值，在 Bekenstein-Hawking 熵 $S_0$ 中，这种似乎的病态通常归因于缺失的非微扰效应。 实际上，我们证明了对于任何具有系综描述的有效量子引力理论，这种情况都必须发生。 为此，我们将通常的引力熵识别为退火熵 $S_a$，并证明如果且仅当基态能量由超对称保护时，这个量在极端情况下给出 $S_0$，否则它会负向发散。 实际表现出热力学行为的是平均或淬火熵 $S_q$，在引力中对其计算的理解尚不清楚：它涉及一个拓扑展开失效的区域中的复制虫洞。 利用矩阵积分，我们发现了新的瞬子鞍点，它们在 $T\sim e^{-S_0}$ 处主导引力相关函数，并且与涉及动力学膜的半经典虫洞对偶。 这些膜解对任何非常接近极端情况的黑洞给出了主要贡献，如果没有它们，与矩阵系综的对偶关系将没有意义。 在非BPS情形下，它们需要使$S_q$非负，并且增强$S_a$的负性，这两种效应与精确计算的矩阵积分结果一致。 我们的瞬子结果通过与$\mathcal{N}=4$超对称杨-米尔斯理论中多重缠绕Wilson圈对应的D3-膜的现场作用量进行测试，发现精确匹配。 我们对低能随机矩阵谱的分析也解释了超对称理论中谱隙的起源，不仅当存在零能BPS态时如此，对于纯非BPS超多重态也是如此。 在前者中，我们关于谱隙的预测——用BPS态的简并度来表示——与$\mathcal{N}=2$超对称JT引力中带隙多重态的R电荷标度一致。 显示英文摘要

摘要： The black hole entropy has been observed to generically turn negative at exponentially low temperatures $T\sim e^{-S_0}$ in the extremal Bekenstein-Hawking entropy $S_0$, a seeming pathology often attributed to missing non-perturbative effects. In fact, we show that this negativity must happen for any effective theory of quantum gravity with an ensemble description. To do so, we identify the usual gravitational entropy as an annealed entropy $S_a$, and prove that this quantity gives $S_0$ at extremality if and only if the ground-state energy is protected by supersymmetry, and diverges negatively otherwise. The actual thermodynamically-behaved quantity is the average or quenched entropy $S_q$, whose calculation is poorly understood in gravity: it involves replica wormholes in a regime where the topological expansion breaks down. Using matrix integrals we find new instanton saddles that dominate gravitational correlators at $T\sim e^{-S_0}$ and are dual to semiclassical wormholes involving dynamical branes. These brane solutions give the leading contribution to any black hole very near extremality, and a duality with matrix ensembles would not make sense without them. In the non-BPS case, they are required to make $S_q$ non-negative and also enhance the negativity of $S_a$, both effects consistent with matrix integrals evaluated exactly. Our instanton results are tested against the on-shell action of D3-branes dual to multiply wrapped Wilson loops in $\mathcal{N}=4$ super-YM, and a precise match is found. Our analysis of low-energy random matrix spectra also explains the origin of spectral gaps in supersymmetric theories, not only when there are BPS states at zero energy, but also for purely non-BPS supermultiplets. In the former, our prediction for the gap in terms of the degeneracy of BPS states agrees with the R-charge scaling in gapped multiplets of $\mathcal{N}=2$ super-JT gravity.