等变体积极值化与全息
Equivariant volume extremization and holography
AI总结：
本文以内部几何或锥的等变体积表述全息引力极值化，通过缠绕四维轨形的膜超引力解验证其可恢复并预测中心荷与自由能，且证实 M5、D4 膜引力块公式。
摘要：
在先前的一篇论文中，我们中的两人（D.M. 和 A.Z.）提出，全息中一大类引力极值化问题可以用内部几何或其上方锥的等变体积来表述。我们通过分析 M 理论以及 II 型超引力中对应于部分或完全缠绕在四维轨形上的膜的超引力解，来证实这一主张。我们表明，我们的方法恢复了若干已知超引力解的相关引力中心荷/自由能，并且也可用于计算那些尚未被显式构造的解的这些量。此外，我们证明了先前猜想的关于 M5 和 D4 膜的引力块公式的有效性。在 M5 膜情形中，我们与一种基于用 Killing 旋量双线性构造的等变形式局域化的近期方法建立了联系。
英文摘要：
In a previous paper two of us (D.M. and A.Z.) proposed that a vast class of gravitational extremization problems in holography can be formulated in terms of the equivariant volume of the internal geometry, or of the cone over it. We substantiate this claim by analysing supergravity solutions corresponding to branes partially or totally wrapped on a four-dimensional orbifold, both in M-theory as well as in type II supergravities. We show that our approach recovers the relevant gravitational central charges/free energies of several known supergravity solutions and can be used to compute these also for solutions that are not known explicitly. Moreover, we demonstrate the validity of previously conjectured gravitational block formulas for M5 and D4 branes. In the case of M5 branes we make contact with a recent approach based on localization of equivariant forms, constructed with Killing spinor bilinears.
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