Relevant Perturbation of Entanglement Entropy and Stationarity

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 Poincare symmetry.

11 pages, 2 figures: v2: minor changes, a reference added

References in corpus (4)

• Holographic c-theorems in arbitrary dimensions
• On Shape Dependence and RG Flow of Entanglement Entropy
• Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT
• Renyi Entropy and Geometry

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• The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields
• Entanglement entropy between real and virtual particles in ${\varphi }^4$ quantum field theory
• Entanglement entropy and complexity of singular subregions in deformed CFT
• Relevant perturbation of entanglement entropy of singular surfaces
• Entanglement entropy of a superflow