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 analyses. 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 the use of 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 cannot 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.
Highlights
It is found by Hung, Myers and Smolkin that there is entropy discrepancy between the field theoretical and the holographic results for the CFTs in 6d spacetime
We briefly review the HMS mismatch [1]. It was found by Hung, Myers and Smolkin find that the logarithmic term of entanglement entropy derived from the field theoretical approach does not match the holographic result for 6d CFTs [1]
In the field theoretical approach, the logarithmic term of EE can be derived as the entropy of the Weyl anomaly [1, 5]
Summary
We briefly review the HMS mismatch [1]. It was found by Hung, Myers and Smolkin find that the logarithmic term of entanglement entropy derived from the field theoretical approach does not match the holographic result for 6d CFTs [1]. HMS focus on the cases with zero extrinsic curvature. In the field theoretical approach, the logarithmic term of EE can be derived as the entropy of the Weyl anomaly [1, 5]. The trace anomaly takes the following form. For entangling surfaces with the rotational symmetry, only Wald entropy contributes to holographic entanglement entropy.
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