Entanglement of heavy quark impurities and generalized gravitational entropy

TL;DR

This paper investigates how heavy quark impurities affect entanglement entropy in N=4 SUSY Yang-Mills theory using holographic methods, revealing complex flow behaviors and universal corrections related to impurity representations.

Contribution

It applies generalized gravitational entropy to non-conformal D-brane embeddings, analyzing entanglement entropy flows for various heavy quark impurity representations in a holographic setting.

Findings

EE excess decreases non-monotonically for D5-branes from UV to IR

EE excess increases for certain D3-brane embeddings, decreases for others

Probe free energy increases monotonically towards IR, supporting its interpretation as relative entropy

Abstract

We calculate the contribution from non-conformal heavy quark sources to the entanglement entropy (EE) of a spherical region in N=4 SUSY Yang-Mills theory. We apply the generalized gravitational entropy method to non-conformal probe D-brane embeddings in AdS_5 x S^5, dual to pointlike impurities exhibiting flows between quarks in large-rank tensor representations and the fundamental representation. For the D5-brane embedding which describes the screening of fundamental quarks in the UV to the antisymmetric tensor representation in the IR, the EE excess decreases non-monotonically towards its IR asymptotic value, tracking the qualitative behaviour of the one-point function of static fields sourced by the impurity. We also examine two classes of D3-brane embeddings, one which connects a symmetric representation source in the UV to fundamental quarks in the IR, and a second category which yields the symmetric representation source on the Coulomb branch. The EE excess for the former increases from the UV to the IR, whilst decreasing and becoming negative for the latter. In all cases, the probe free energy on hyperbolic space with \beta=2\pi, increases monotonically towards the IR, supporting its interpretation as a relative entropy. We identify universal corrections, depending logarithmically on the VEV, for the symmetric representation on the Coulomb branch.