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Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy
by Alexey Milekhin, Amirhossein Tajdini
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Submission summary
| Authors (as registered SciPost users): | Alexey Milekhin |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202302_00034v1 (pdf) |
| Date accepted: | 2023-04-18 |
| Date submitted: | 2023-02-22 05:35 |
| Submitted by: | Milekhin, Alexey |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
List of changes
We thank the referees for carefully reading the manuscript and providing very useful comments. Here is the full list of changes:
1) Eq. (2.1) is made more clear.
2) The discussion on non-Abelian computation between eqns. (5.33) and (5.37) is substantially improved.
3) Unfortunately, it would be hard to perform several-replica computation of $<e^{i \alpha Q_R}>$ because of the possible replica wormholes. We added a comment on that after eq. (5.14).
4) The first paragraph of Section 4.2 now includes the discussion of having finite temperature instead of zero-temperature. This is a very important point and we acknowledged that it was the referee's suggestion.
5) Above eq. (2.5) "moments" is changed to "characteristic function".
Published as SciPost Phys. 14, 172 (2023)