TY - JOUR

T1 - Entanglement as a probe of confinement

AU - Klebanov, Igor R.

AU - Kutasov, David

AU - Murugan, Arvind

N1 - Funding Information:
We are grateful to Marcus Benna, Oleg Lunin, Juan Maldacena, Dmitry Malyshev and Tadashi Takayanagi for useful discussions. I.K. acknowledges the hospitality of the University of Tokyo, Komaba, and the Aspen Center for Physics, where some of his work on this project was carried out. A.M. and D.K. acknowledge the hospitality of TASI, Boulder where some of this work was carried out. The work of I.K. and A.M. was supported in part by the National Science Foundation under Grant No. PHY-0243680. The work of D.K. is supported in part by the Department of Energy under grant DE-FG02-90ER40560, the National Science Foundation under grant 0529954 and the Joint Theory Institute funded by Argonne National Laboratory and the University of Chicago. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of these funding agencies.

PY - 2008/6/11

Y1 - 2008/6/11

N2 - We investigate the entanglement entropy in gravity duals of confining large Nc 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 lcrit while the connected one dominates below that value. The change of behavior at l = lcrit is reminiscent of the finite temperature deconfinement transition: for l < lcrit the entropy scales as Nc2, while for l > 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.

AB - We investigate the entanglement entropy in gravity duals of confining large Nc 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 lcrit while the connected one dominates below that value. The change of behavior at l = lcrit is reminiscent of the finite temperature deconfinement transition: for l < lcrit the entropy scales as Nc2, while for l > 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.

KW - Color confinement

KW - Entanglement entropy

KW - Gauge/string duality

KW - Large N gauge theory

KW - Phase transition

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U2 - 10.1016/j.nuclphysb.2007.12.017

DO - 10.1016/j.nuclphysb.2007.12.017

M3 - Article

AN - SCOPUS:39749154770

SN - 0550-3213

VL - 796

SP - 274

EP - 293

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 1-2

ER -