A note on the resolution of the entropy discrepancy

TL;DR

This paper examines two proposed solutions to the entropy discrepancy in 6D conformal field theories, finding that the entanglement entropy approach fails and highlighting issues with the Wald entropy formula on certain horizons.

Contribution

The paper critically evaluates two recent proposals for resolving the HMS entropy puzzle, demonstrating limitations of the entanglement entropy method and issues with Wald entropy in specific geometries.

Findings

The entanglement entropy approach cannot resolve the HMS puzzle.

Wald entropy is not well-defined on horizons with extrinsic curvature.

The second proposal does not successfully address the entropy discrepancy.

Abstract

It was found by Hung, Myers and Smolkin that there is entropy discrepancy for the CFTs in 6-dimensional space-time, between the field theoretical and the holographic analysis. Recently, two different resolutions to this puzzle have been proposed. One of them suggests to utilize the anomaly-like entropy and the generalized Wald entropy to resolve the HMS puzzle, while the other one initiates to use the entanglement entropy which arises from total derivative terms in the Weyl anomaly to explain the HMS mismatch. We investigate these two proposals carefully in this note. By studying the CFTs dual to Einstein gravity, we find that the second proposal can not solve the HMS puzzle. Moreover, the Wald entropy formula is not well-defined on horizon with extrinsic curvatures, in the sense that, in general, it gives different results for equivalent actions.