Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT

TL;DR

This paper derives exact and numerical results for entanglement entropy in (5+1)-dimensional conformal field theories, exploring shape dependence, anomalies, and holographic methods, with applications to M5-branes and free theories.

Contribution

It provides the first comprehensive calculation of shape-dependent entanglement entropy in (5+1)-dimensional CFTs, including holographic and numerical analyses.

Findings

Shape dependence expressed via extrinsic curvature and conical singularities.

Holographic calculations using Lovelock gravity match field theory results.

Numerical verification of entanglement entropy relations and the F-theorem.

Abstract

We calculate the shape dependence of entanglement entropy in (5+1)-dimensional conformal field theory in terms of the extrinsic curvature of the entangling surface, the opening angles of possible conical singularities, and the conformal anomaly coefficients, which are required to obey a single constraint. An important special case of this result is given by the interacting (2,0) theory describing a large number of coincident M5-branes. To derive the more general result we rely crucially on the holographic prescription for calculating entanglement entropy using Lovelock gravity. We test the conjecture by relating the entanglement entropy of the free massless (1,0) hypermultiplet in (5+1)-dimensions to the entanglement entropy of the free massive chiral multiplet in (2+1)-dimensions, which we calculate numerically using lattice techniques. We also present a numerical calculation of the (2+1)-dimensional renormalized entanglement entropy for the free massive Dirac fermion, which is shown to be consistent with the F-theorem.