Holographic flows and thermodynamics of Polyakov loop impurities

Abstract

We study holographic probes dual to heavy quark impurities interpolating between fundamental and symmetric/antisymmetric tensor representations in strongly coupled N = 4 supersymmetric gauge theory. These correspond to non-conformal D3-and D5-brane probe embeddings in AdS 5 × S 5 exhibiting flows on their world-volumes. By examining the asymptotic regimes of the embeddings and the one-point function of static fields sourced by the boundary impurity, we conclude that the D5-brane embedding describes the screening of fundamental quarks in the UV into an antisymmetric source in the IR, whilst the non-conformal, D3-brane solution interpolates between the symmetric representation in the UV and fundamental sources in the IR. The D5-brane embeddings exhibit nontrivial thermodynamics with multiple branches of solutions, whilst the thermal analogue of the interpolating D3-brane solution does not appear to exist.

Entanglement of heavy quark impurities and generalized gravitational entropy

“…Our aim will be to reproduce these results for the conformal impurities using the method of [15] and then apply the same to the case of the non-conformal impurity flows that were discussed in [23].…”

“…This is realized geometrically, by having the D5-brane wrapping an S 4 latitude of the five-sphere in AdS 5 × S 5 . In the non-conformal "flow" solution described in [23], the polar angle θ associated to this S 4 latitude varies as a function of the radial position in AdS 5 . We can choose the worldvolume coordinates to be (σ, x 0 , Ω 4 ), where σ parametrises the non-compact spatial coordinate on the brane.…”

“…• For the D3-brane probes, a simple BPS deformation exists which was discussed relatively recently in [24] and [23]. There are two categories of these solutions (figure 1): one yields a symmetric representation (S k ) source in the UV "dissociating" into k coincident quarks in the IR, while the second category describes a heavy quark in representation S k on the Coulomb branch of the N = 4 theory with SU(N ) broken to U(1) × SU(N − 1).…”

“…The embedding admits a deformation which can be interpreted as an RG flow on the worldvolume of the impurity [23]. Our goal will be to extract the behaviour of the impurity EE along this flow.…”

“…The counterterms can be split in two pieces: one which regulates the UV divergences in the action and another which fixes the number of units of string charge carried by the embedding to be k ∈ Z [17,23],…”