Entanglement as a Probe of Confinement

TL;DR

The paper investigates entanglement entropy in gravity duals of confining large N_c gauge theories using a holographic minimal-surface prescription. It shows that confining geometries generically admit two competing extremal surfaces for a strip: a connected tube and a pair of disconnected ends, producing a first-order phase transition at l_crit that changes the S_A scaling from O(N_c^2) to O(N_c^0). The authors analyze several explicit backgrounds (D4 on a circle, D3 on a circle, and the KS cascading theory) and extract l_crit and l_max, illustrating how the transition signals confinement and is tied to the density of states (Hagedorn behavior) in the dual field theory. They argue that such a phase structure should be a universal feature of confining gravity duals and propose that entanglement entropy can serve as a constraint on viable holographic models.

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.

Figures (6)

• Figure 1: $l(U^*)$ for $D4$-branes on a circle.
• Figure 2: Entropies of the connected (blue and red) and disconnected (black) solutions for the wrapped $D4$-brane geometry.
• Figure 3: $l(U_*)$ for $D3$-branes on a circle.
• Figure 4: Entropies of the connected (blue and red) and disconnected (black) solutions for the wrapped $D3$-brane geometry.
• Figure 5: $l(\tau_*)$ for the KS geometry.