In this paper we use Euclidean gravity to derive a simple formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero density, this gives a new proof of the completeness hypothesis for finite gauge fields. Inspired by the generality of the argument we further propose that the formula applies at high energy in any quantum field theory with a finite-group global symmetry, and give some evidence for this conjecture.

中文翻译：

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有限群对称理论中状态密度的通用公式

在本文中，我们使用欧几里得引力推导出黑洞微态密度的简单公式，该微态在任何有限规范群的每个不可约表示中进行变换。由于每个表示都以非零密度出现，这为有限规范场的完备性假设提供了新的证明。受论点普遍性的启发，我们进一步提出该公式适用于任何具有有限群全局对称性的量子场论的高能量，并为该猜想提供了一些证据。