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arXiv 1806.04479hep-th
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超引力中的扭曲和定域化:BPS黑洞的等变上同调

Twisting and localization in supergravity: equivariant cohomology of BPS black holes

Imtak Jeon, Sameer Murthy

摘要:

我们使用最近在arxiv:1806.03690中制定的超对称背景下定义的变形BRST代数,发展了超引力中超对称局部化的形式主义。引力泛函积分局部化到全局超荷$Q_\text{eq}$的上同调上,服从$Q_\text{eq}^2=H$,其中$H$是背景的全局对称性。只要超对称性可以在壳外实现,我们的构造自然会产生一种扭曲的超引力。我们给出了四维N=2超引力场超共形表述的扭曲引力子多重态和鬼场的详细情况。作为该方法的一个应用,我们系统地计算了超对称黑洞的精确量子熵。特别地,我们计算了$Q_\text{eq} \mathcal{V}$变形算子的单圈行列式,用于外尔多重态围绕$AdS_2 \times S^2$鞍的离壳波动。这一结果与相应的大电荷在壳层分析结果是一致的,是完成量子熵的第一性原理计算所必需的。

英文摘要:

We develop the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background as recently formulated in arxiv:1806.03690. The gravitational functional integral localizes onto the cohomology of a global supercharge $Q_\text{eq}$, obeying $Q_\text{eq}^2=H$, where $H$ is a global symmetry of the background. Our construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. We present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the $Q_\text{eq} \mathcal{V}$ deformation operator for the off-shell fluctuations of the Weyl multiplet around the $AdS_2 \times S^2$ saddle. This result, which is consistent with the corresponding large-charge on-shell analysis, is needed to complete the first-principles computation of the quantum entropy.

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