标题： 超重力中奇数维的等变局部化 显示英文标题

标题： Equivariant localization in supergravity in odd dimensions

摘要： 我们讨论了在具有边界的奇数维流形上某些积分的局部化公式，这些流形配备了一个Killing向量，并利用此公式将五维最小规范超引力的大量超对称解的正则化在壳作用量进行局部化。 具体来说，我们考虑时间类渐近AdS_5的解，在这些解中假设横向Kähler叶状结构是环面的。 我们发现背景减法正则化方法导致了一个有趣的在壳作用量公式，该公式涉及Martelli-Sparks-Yau Sasakian体积的解析延拓。 特别是，我们表明正则化的在壳作用量是一个有效紧致五维流形的环面数据以及对应双锥体之外的超对称Killing向量的函数。 作为我们的主要例子，我们仅使用拓扑数据推导了AdS_5中超对称和旋转黑洞的著名熵函数。 显示英文摘要

摘要： We discuss a localization formula for certain integrals on odd-dimensional manifolds with boundaries, equipped with a Killing vector, and employ this to localize the regularised on-shell action of a large class of supersymmetric solutions of five dimensional minimal gauged supergravity. Specifically, we consider asymptotically AdS_5 solutions in the time-like class, in which the transverse K\"ahler foliation is assumed to be toric. We find that the background subtraction regularization method leads to an intriguing formula for the on-shell action, in terms of an analytic continuation of the Martelli-Sparks-Yau Sasakian volume. In particular, we show that the regularised on-shell action is a function of the toric data of an effective compact five-dimensional manifold, as well as of the supersymmetric Killing vector, outside the corresponding dual cone. As our main example we provide a derivation of the well-known entropy function of supersymmetric and rotating black holes in AdS_5, using only topological data.