Abstract
We calculate the contribution from non-conformal heavy quark sources to the entanglement entropy (EE) of a spherical region in mathcal{N}=4 SUSY Yang-Mills theory. We apply the generalized gravitational entropy method to non-conformal probe D-brane embeddings in AdS5×S5, 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 β = 2π 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.
Highlights
Geometry, which could be a compact Euclidean time direction, varying its periodicity in a well-defined manner and calculating the resulting variation in the action so as to obtain a gravitational or geometric entropy
In this paper we will apply the method of [15] based on gravitational entropy contributions to obtain the entanglement entropy (EE) excess due to the corresponding probes (D-branes) in the gravity dual, including the effect of deformations that trigger flows on the impurity
We focus attention on heavy quark probes in the symmetric and antisymmetric tensor representations of rank k, with k ∼ O(N ), which are dual to D3 and D5-brane probes in AdS5×S5
Summary
It was argued in [15] that the entanglement entropy contribution from a finite number Nf of flavour degrees of freedom, introduced into a large-N CFT (with a holographic gravity dual), can be computed without having to consider explicit backreaction of flavour fields. The classical action for these geometries yields the holographic entanglement entropy via, S(Ad−1) = − n∂n [log Z(n) − n log Z(1)]|n=1 This quantity only receives non-zero contribution from a boundary term within the bulk, arising from the locus of points where the circle shrinks. Computed holographically by the classical action of the bulk Euclidean AdSd+1 geometry with hyperbolic slices, the replica trick is implemented by allowing the inverse temperature of the hyperbolic black hole to deviate from the value β = 2π: log ZH = −IAdS(β). The excess contribution from such an impurity to the EE of a spherical region in N = 4 SYM was calculated in [16] using the method described above, leading to eq (2.3) but where ZH is replaced by the impurity partition function in hyperbolic space, computed by a Polyakov loop or circular Wilson loop W◦. Our aim will be to reproduce these results for the conformal impurities using the method of [15] and apply the same to the case of the non-conformal impurity flows that were discussed in [23]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
