Entanglement Entropy for Relevant and Geometric Perturbations

TL;DR

The paper develops a perturbative, field-theoretic framework to compute entanglement entropy under two classes of deformations: relevant perturbations of a CFT and small geometric deformations of the entangling surface in flat space. It derives a universal second-order contribution to S for a CFT perturbed by a relevant operator, valid across all CFTs, and tests it with a free scalar as well as holographic expectations. In the geometric sector, it constructs the second-order form of the universal entanglement entropy under surface and background deformations, obtaining a Weyl-invariant expression that, however, conflicts with Solodukhin’s known result, suggesting possible missing boundary or contact-term contributions. The work highlights deep issues about universality, boundary terms, and the proper treatment of contact terms in entanglement entropy, pointing to future investigations into boundary physics and Rényi entropy as avenues to resolve the tensions.

Abstract

We continue the study of entanglement entropy for a QFT through a perturbative expansion of the path integral definition of the reduced density matrix. The universal entanglement entropy for a CFT perturbed by a relevant operator is calculated to second order in the coupling. We also explore the geometric dependence of entanglement entropy for a deformed planar entangling surface, finding surprises at second order.

Figures (1)

• Figure 1: (a) An entangling surface $\Sigma$ that is a plane. We use coordinates $x_{\mu} = (x_a,y_i)$, with $x_a$ transverse to the plane and $y_i$ along the plane. (b) The transverse space to the plane.