Entanglement as a probe of confinement

We investigate the entanglement entropy in gravity duals of confining large NcNc gauge theories using the proposal of [S. Ryu, T. Takayanagi, Phys. Rev. Lett. 96 (2006) 181602, hep-th/0603001; S. Ryu, T. Takayanagi, JHEP 0608 (2006) 045, 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 lcritlcrit while the connected one dominates below that value. The change of behavior at l=lcritl=lcrit is reminiscent of the finite temperature deconfinement transition: for llcritl>lcrit as Nc0. 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.