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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
We derive the universal terms of entanglement entropy for 6d CFTs by applying
the holographic and the field theoretical approaches, respectively. Our
formulas are conformal invariant and agree with the results of [34,35].
Remarkably, we find that the holographic and the field theoretical results
match exactly for the $C^2$ and $Ck^2$ terms. Here $C$ and $k$ denote the Weyl
tensor and the extrinsic curvature, respectively. As for the $k^4$ terms, we
meet the splitting problem of the conical metrics. The splitting problem in the
bulk can be fixed by equations of motion. As for the splitting on the boundary,
we assume the general forms and find that there indeed exists suitable
splitting which can make the holographic and the field theoretical $k^4$ terms
match. Since we have much more equations than the free parameters, the match
for $k^4$ terms is non-trivial.
