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Relevant perturbation of entanglement entropy and stationarity

School of Natural Sciences, Institute For Advanced Study, Princeton, New Jersey 08540, USA

Phys. Rev. D 90, 045006 – Published 4 August, 2014

DOI: https://doi.org/10.1103/PhysRevD.90.045006

Abstract

A relevant perturbation of the entanglement entropy of a sphere is examined holographically near the UV fixed point. Varying the conformal dimension of the relevant operator, we obtain three different sectors: (1) the entanglement entropy is stationary and the perturbative expansion is well defined with respect to the relevant coupling, (2) the entropy is stationary, but the perturbation fails, (3) the entropy is neither stationary nor perturbative. We compare our holographic results with the numerical calculation for a free massive scalar field in three dimensions, and find a qualitative agreement between them. We speculate that these statements hold for any relevant perturbation in any quantum field theory invariant under the Poincaré symmetry.

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Relevant perturbation of entanglement entropy and stationarity

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