Relevant Perturbation of Entanglement Entropy and Stationarity

TL;DR

This paper investigates how relevant perturbations affect entanglement entropy near the UV fixed point using holographic methods, revealing different behaviors depending on the conformal dimension and comparing with free scalar field results.

Contribution

It classifies the behavior of entanglement entropy under relevant perturbations into three sectors and compares holographic predictions with numerical scalar field calculations.

Findings

Entanglement entropy can be stationary or non-stationary depending on the perturbation.

Different sectors exhibit distinct perturbative behaviors.

Qualitative agreement between holographic and scalar field results was observed.

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.