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2020

R\'enyi entropies and area operator from gravity with Hayward term

Botta-Cantcheff, Marcelo, Martinez, Pedro J., Zarate, Juan F.

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In the context of the holographic duality, the entanglement entropy of ordinary QFT in a subregion in the boundary is given by a quarter of the area of an minimal surface embedded in the bulk spacetime.

This rule has been also extended to a suitable one-parameter generalization of the von-Neuman entropy $\hat{S}_n$ that is related to the R\'enyi entropies $S_n$, as given by the area of a \emph{cosmic brane} minimally coupled with gravity, with a tension related to $n$ that vanishes as $n\to1$, and moreover, this parameter can be analytically extended to arbitrary real values.
However, the brane action plays no role in the duality and cannot be considered a part of the theory of gravity, thus it is used as an auxiliary tool to find the correct background geometry.
In this work we study the construction of the gravitational (reduced) density matrix from holographic states, whose wave-functionals are described as euclidean path integrals with arbitrary conditions on the asymptotic boundaries, and argue that in general, a non-trivial Hayward term must be haven into account.

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