A note on the resolution of 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.

12 pages, no figures, accepted by PLB

References in corpus (3)

• Entropy vs Gravitational Action: Do Total Derivatives Matter?
• Entropy discrepancy and total derivatives in trace anomaly
• Generalized Gravitational Entropy from Total Derivative Action

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• A Quantum Focussing Conjecture
• A Second Law for Higher Curvature Gravity
• The holographic entropy increases in quadratic curvature gravity
• f(Lovelock) theories of gravity
• Mutual information and the F-theorem
• Holographic entanglement entropy for perturbative higher-curvature gravities
• Holographic Entanglement for Chern-Simons Terms
• Entropy for gravitational Chern-Simons terms by squashed cone method
• Entropy discrepancy and total derivatives in trace anomaly
• Universal Terms of Entanglement Entropy for 6d CFTs
• Generalized Gravitational Entropy from Total Derivative Action
• Topological Entanglement Entropy, Ground State Degeneracy and Holography