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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
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. Recently, there appears two different proposals for the resolution
of this puzzle. One proposes to use the anomaly of entropy and the generalized
Wald entropy to resolve the HMS puzzle. While the other one suggests to use the
entropy of total derivatives to explain the HMS mismatch. We investigate these
two proposals carefully in this note. By studying the example of Einstein
gravity, we find that it is the proposal of [2] rather than the one of [3,4]
that can solve the HMS puzzle. Besides, we find that there is arbitrariness in
the derivations of Wald entropy. And only the total entropy is well-defined.
