Abstract
We compute holographic entanglement entropy in two strongly coupled non-local field theories: the dipole and the noncommutative deformations of SYM theory. We find that entanglement entropy in the dipole theory follows a volume law for regions smaller than the length scale of nonlocality and has a smooth cross-over to an area law for larger regions. In contrast, in the noncommutative theory the entanglement entropy follows a volume law for up to a critical length scale at which a phase transition to an area law occurs. The critical length scale increases as the UV cutoff is raised, which is indicative of UV/IR mixing and implies that entanglement entropy in the noncommutative theory follows a volume law for arbitrary large regions when the size of the region is fixed as the UV cutoff is removed to infinity. Comparison of behaviour between these two theories allows us to explain the origin of the volume law. Since our holographic duals are not asymptotically AdS, minimal area surfaces used to compute holographic entanglement entropy have novel behaviours near the boundary of the dual spacetime. We discuss implications of our results on the scrambling (thermalization) behaviour of these nonlocal field theories.
Similar content being viewed by others
References
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
T. Nishioka, S. Ryu and T. Takayanagi, Holographic entanglement entropy: an overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].
T. Takayanagi, Entanglement entropy from a holographic viewpoint, Class. Quant. Grav. 29 (2012) 153001 [arXiv:1204.2450] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
T. Nishioka and T. Takayanagi, AdS bubbles, entropy and closed string tachyons, JHEP 01 (2007) 090 [hep-th/0611035] [INSPIRE].
I.R. Klebanov, D. Kutasov and A. Murugan, Entanglement as a probe of confinement, Nucl. Phys. B 796 (2008) 274 [arXiv:0709.2140] [INSPIRE].
J. Eisert, M. Cramer and M. Plenio, Area laws for the entanglement entropy — A review, Rev. Mod. Phys. 82 (2010) 277 [arXiv:0808.3773] [INSPIRE].
J.L. Barbon and C.A. Fuertes, Holographic entanglement entropy probes (non)locality, JHEP 04 (2008) 096 [arXiv:0803.1928] [INSPIRE].
N. Lashkari, Equilibration of small and large subsystems in field theories and matrix models, arXiv:1304.6416 [INSPIRE].
Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
M. Requardt, Entanglement-entropy for groundstates, low-lying and highly excited eigenstates of general (lattice) hamiltonians, hep-th/0605142 [INSPIRE].
V. Alba, M. Fagotti and P. Calabrese, Entanglement entropy of excited states, J. Stat. Mech. (2009) P10020 [arXiv:0909.1999].
M. Edalati, W. Fischler, J.F. Pedraza and W. Tangarife Garcia, Fast scramblers and non-commutative gauge theories, JHEP 07 (2012) 043 [arXiv:1204.5748] [INSPIRE].
J.L. Barbon and C.A. Fuertes, A note on the extensivity of the holographic entanglement entropy, JHEP 05 (2008) 053 [arXiv:0801.2153] [INSPIRE].
W. Fischler, A. Kundu and S. Kundu, Holographic entanglement in a noncommutative gauge theory, arXiv:1307.2932 [INSPIRE].
A. Hashimoto and N. Itzhaki, Noncommutative Yang-Mills and the AdS/CFT correspondence, Phys. Lett. B 465 (1999) 142 [hep-th/9907166] [INSPIRE].
J.M. Maldacena and J.G. Russo, Large-N limit of noncommutative gauge theories, JHEP 09 (1999) 025 [hep-th/9908134] [INSPIRE].
S. Minwalla, M. Van Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics, JHEP 02 (2000) 020 [hep-th/9912072] [INSPIRE].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
M. Li and Y.-S. Wu, Holography and noncommutative Yang-Mills, Phys. Rev. Lett. 84 (2000) 2084 [hep-th/9909085] [INSPIRE].
S. Chakravarty, K. Dasgupta, O.J. Ganor and G. Rajesh, Pinned branes and new non-Lorentz invariant theories, Nucl. Phys. B 587 (2000) 228 [hep-th/0002175] [INSPIRE].
A. Bergman and O.J. Ganor, Dipoles, twists and noncommutative gauge theory, JHEP 10 (2000) 018 [hep-th/0008030] [INSPIRE].
K. Dasgupta, O.J. Ganor and G. Rajesh, Vector deformations of N = 4 super Yang-Mills theory, pinned branes and arched strings, JHEP 04 (2001) 034 [hep-th/0010072] [INSPIRE].
A. Bergman, K. Dasgupta, O.J. Ganor, J.L. Karczmarek and G. Rajesh, Nonlocal field theories and their gravity duals, Phys. Rev. D 65 (2002) 066005 [hep-th/0103090] [INSPIRE].
E. Bergshoeff, C.M. Hull and T. Ortín, Duality in the type-II superstring effective action, Nucl. Phys. B 451 (1995) 547 [hep-th/9504081] [INSPIRE].
K. Dasgupta and M. Sheikh-Jabbari, Noncommutative dipole field theories, JHEP 02 (2002) 002 [hep-th/0112064] [INSPIRE].
K. Narayan, T. Takayanagi and S.P. Trivedi, AdS plane waves and entanglement entropy, JHEP 04 (2013) 051 [arXiv:1212.4328] [INSPIRE].
V.E. Hubeny, H. Maxfield, M. Rangamani and E. Tonni, Holographic entanglement plateaux, JHEP 08 (2013) 092 [arXiv:1306.4004] [INSPIRE].
M. Headrick, Entanglement Renyi entropies in holographic theories, Phys. Rev. D 82 (2010) 126010 [arXiv:1006.0047] [INSPIRE].
E. Tonni, Holographic entanglement entropy: near horizon geometry and disconnected regions, JHEP 05 (2011) 004 [arXiv:1011.0166] [INSPIRE].
W. Fischler, A. Kundu and S. Kundu, Holographic mutual information at finite temperature, Phys. Rev. D 87 (2013) 126012 [arXiv:1212.4764] [INSPIRE].
R. Bousso, S. Leichenauer and V. Rosenhaus, Light-sheets and AdS/CFT, Phys. Rev. D 86 (2012) 046009 [arXiv:1203.6619] [INSPIRE].
B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The gravity dual of a density matrix, Class. Quant. Grav. 29 (2012) 155009 [arXiv:1204.1330] [INSPIRE].
V.E. Hubeny and M. Rangamani, Causal holographic information, JHEP 06 (2012) 114 [arXiv:1204.1698] [INSPIRE].
R. Bousso, B. Freivogel, S. Leichenauer, V. Rosenhaus and C. Zukowski, Null geodesics, local CFT operators and AdS/CFT for subregions, Phys. Rev. D 88 (2013) 064057 [arXiv:1209.4641] [INSPIRE].
A. Hashimoto and N. Itzhaki, Traveling faster than the speed of light in noncommutative geometry, Phys. Rev. D 63 (2001) 126004 [hep-th/0012093] [INSPIRE].
B. Durhuus and T. Jonsson, Noncommutative waves have infinite propagation speed, JHEP 10 (2004) 050 [hep-th/0408190] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
A.C. Wall, Maximin surfaces and the strong subadditivity of the covariant holographic entanglement entropy, arXiv:1211.3494 [INSPIRE].
M. Headrick and T. Takayanagi, A holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev. D 76 (2007) 106013 [arXiv:0704.3719] [INSPIRE].
W. Li and T. Takayanagi, Holography and entanglement in flat spacetime, Phys. Rev. Lett. 106 (2011) 141301 [arXiv:1010.3700] [INSPIRE].
V.E. Hubeny, Extremal surfaces as bulk probes in AdS/CFT, JHEP 07 (2012) 093 [arXiv:1203.1044] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1307.3517
Rights and permissions
About this article
Cite this article
Karczmarek, J.L., Rabideau, C. Holographic entanglement entropy in nonlocal theories. J. High Energ. Phys. 2013, 78 (2013). https://doi.org/10.1007/JHEP10(2013)078
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2013)078