A universal formula for the density of states in theories with finite-group symmetry

TL;DR

This paper derives a universal formula for the density of black hole microstates transforming under finite-group symmetries using Euclidean gravity, providing a new proof of the completeness hypothesis and proposing broader applicability in quantum field theories.

Contribution

It introduces a universal formula for the density of states in theories with finite-group symmetry, linking gravity and quantum field theory insights.

Findings

Formula applies to black hole microstates in finite gauge groups

Provides proof of the completeness hypothesis for finite gauge fields

Suggests the formula's applicability to high-energy quantum field theories with finite symmetries

Abstract

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.