Entanglement entropy and differential entropy for massive flavors

TL;DR

This paper computes holographic entanglement entropy for massive flavors in the D3-D7 system, confirming universal terms match conformal perturbation theory and introducing a new method for such calculations in brane probe systems.

Contribution

It introduces a new holographic method for computing entanglement entropy in brane probe systems and analyzes differential entropy's relation to lower-dimensional metrics.

Findings

Universal entanglement entropy terms match conformal perturbation theory.

New method for entanglement entropy calculation using Kaluza-Klein holography.

Differential entropy reflects the effective lower-dimensional Einstein metric.

Abstract

In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.