Entanglement as a Probe of Confinement

TL;DR

This paper studies how entanglement entropy behaves in gravity models of confining gauge theories, revealing a phase transition at a critical length that resembles deconfinement, and suggests this can constrain dual gravity models.

Contribution

It demonstrates a phase transition in entanglement entropy in confining backgrounds, linking it to confinement and providing a new criterion for gravity duals of such theories.

Findings

Entanglement entropy exhibits a phase transition at a critical length.

Disconnected surfaces dominate for large segments, connected for small segments.

The entropy scaling changes from N_c^2 to N_c^0 across the transition.

Abstract

We investigate the entanglement entropy in gravity duals of confining large $N_c$ gauge theories using the proposal of arXiv:hep-th/0603001, arXiv:hep-th/0605073. 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 $l_{\rm crit}$ while the connected one dominates below that value. The change of behavior at $l=l_{\rm crit}$ is reminiscent of the finite temperature deconfinement transition: for $l < l_{\rm crit}$ the entropy scales as $N_c^2$, while for $l > l_{\rm crit}$ as $N_c^0$. 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.