Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy

TL;DR

This paper investigates the fluctuation entropy of Hawking radiation in 2D gravity models with internal symmetries, revealing how global and gauge symmetries influence entropy growth and the validity of the island prescription.

Contribution

It introduces a replica-free method to analyze charge fluctuation entropy in 2D gravity, highlighting the impact of symmetries on entropy behavior and the limitations of current island prescriptions.

Findings

Fluctuation entropy exceeds entanglement entropy with global symmetry.

A lower bound on gauge coupling prevents entropy divergence.

Identifies puzzles in applying island prescription with gauge symmetry.

Abstract

We study the fluctuation entropy for two-dimensional matter systems with an internal symmetry coupled to Jackiw--Teitelboim(JT) gravity joined to a Minkowski region. The fluctuation entropy is the Shannon entropy associated to probabilities of finding particular charge for a region. We first consider a case where the matter has a global symmetry. We find that the fluctuation entropy of Hawking radiation shows an unbounded growth and exceeds the entanglement entropy in presence of islands. This indicates that the global symmetry is violated. We then discuss the fluctuation entropy for matter coupled to a two-dimensional gauge field. We find a lower bound on the gauge coupling $g_0$ in order to avoid a similar issue. Also, we point out a few puzzles related to the island prescription in presence of a gauge symmetry.