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

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arxiv 2109.03838 v3 pith:R5ASOTDA submitted 2021-09-08 hep-th cond-mat.str-elgr-qchep-ph

Daniel Harlow , Hirosi Ooguri This is my paper · ORCID
classification hep-thcond-mat.str-elgr-qchep-ph
keywords densityformulafinitefinite-groupgaugerepresentationsymmetryappears
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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.

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    For 2D CFTs with boundary-only symmetry breaking, the entanglement asymmetry is log|G| with power-law corrections for finite groups, (dim G/2) log log(ℓ/ε) for compact Lie groups, and it drops from log|G| to 0 at t=ℓ/...

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