Entanglement as a probe of confinement

Abstract

We investigate the entanglement entropy in gravity duals of confining large N c gauge theories using the proposal of [1]. Dividing one of the directions of space into a line segment of length l and its complement, the entanglement entropy between the two subspaces is given by the classical action of the minimal bulk hypersurface which approaches the endpoints of the line segment at the boundary. We find that in confining backgrounds there are generally two such surfaces. One consists of two disconnected components localized at the endpoints of the line segment. The other contains a tube connecting the two components. The disconnected surface dominates the entropy for l above a certain critical value l crit while the connected one dominates below that value. The change of behavior at l = l crit is reminiscent of the finite temperature deconfinement transition: for l < l crit the entropy scales as N 2 c , while for l > l crit as N 0 c . We argue that a similar transition should occur in any field theory with a Hagedorn spectrum of non-interacting bound states. The requirement that the entanglement entropy has a phase transition may be useful in constraining gravity duals of confining theories.

Holographic flows in non-Abelian T-dual geometries

“…Indeed, using the expressions relating central charges to internal volumes, see [61] and for a generalization to include non-constant dilaton [37] applicable in this case, one finds (normalizing such that…”

“…At the end points of the RG flow this c-function coincides with the central charge and therefore is conjectured to satisfy c U V > c IR . Following [37,61] and according to our normalisations the central charges at the fixed points of the KM solution are…”

Holographic entanglement entropy in general holographic superconductor models

“…This proposal provides a simple and elegant way to calculate the entanglement entropy of a strongly coupled system which has a gravity dual. Since then, there have been a lot of works studying the entanglement entropy in various gravity theories [37][38][39][40][41][42][43][44][45]. Extending the investigation to the holographic superconductors, Albash and Johnson observed in the metal/superconductor system that the entanglement entropy in superconducting case is always less than the one in the metal phase and the entropy as a function of temperature is found to have a discontinuous slop at the transition temperature T c in the case of the second order phase transition [46].…”

Entanglement entropy, trace anomalies and holography

“…Arguments for the validity of this assumption were presented in [4]. Using the aforementioned holographic representation for massive d = 4 theories in [5] information about the phase structure of these theories was obtained; see also [6] for an earlier discussion of this issue.…”