Universal Entanglement and Boundary Geometry in Conformal Field Theory

TL;DR

This paper calculates the universal entanglement entropy for spheres in even-dimensional conformal field theories using boundary terms in the trace anomaly, revealing a boundary effect interpretation.

Contribution

It introduces a boundary-focused approach to compute entanglement entropy and derives explicit boundary terms for the trace anomaly in higher dimensions.

Findings

Universal EE is a boundary effect in conformal field theories.

Derived explicit boundary terms for the trace anomaly in 4D and 6D.

Connected boundary terms to earlier bulk actions in the literature.

Abstract

Employing a conformal map to hyperbolic space cross a circle, we compute the universal contribution to the vacuum entanglement entropy (EE) across a sphere in even-dimensional conformal field theory. Previous attempts to derive the EE in this way were hindered by a lack of knowledge of the appropriate boundary terms in the trace anomaly. In this paper we show that the universal part of the EE can be treated as a purely boundary effect. As a byproduct of our computation, we derive an explicit form for the A-type anomaly contribution to the Wess-Zumino term for the trace anomaly, now including boundary terms. In d=4 and 6, these boundary terms generalize earlier bulk actions derived in the literature.