### Abstract

We investigate the entanglement entropy in gravity duals of confining large N_{c} 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 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_{c}^{2}, while for l > l_{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.

Original language | English (US) |
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Pages (from-to) | 274-293 |

Number of pages | 20 |

Journal | Nuclear Physics B |

Volume | 796 |

Issue number | 1-2 |

DOIs | |

State | Published - Jun 11 2008 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- Color confinement
- Entanglement entropy
- Gauge/string duality
- Large N gauge theory
- Phase transition

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## Cite this

*Nuclear Physics B*,

*796*(1-2), 274-293. https://doi.org/10.1016/j.nuclphysb.2007.12.017