Abstract
In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.
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References
H.S. Snyder, Quantized space-time, Phys. Rev. 71 (1947) 38 [INSPIRE].
T. Banks, W. Fischler, S. Shenker and L. Susskind, M theory as a matrix model: a conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [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].
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
D.J. Gross, A. Hashimoto and N. Itzhaki, Observables of noncommutative gauge theories, Adv. Theor. Math. Phys. 4 (2000) 893 [hep-th/0008075] [INSPIRE].
M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].
J.L.F. Barbon and C.A. Fuertes, Holographic entanglement entropy probes (non)locality, JHEP 04 (2008) 096 [arXiv:0803.1928] [INSPIRE].
M.M. Wolf, F. Verstraete, M.B. Hastings and J.I. Cirac, Area laws in quantum systems: mutual information and correlations, Phys. Rev. Lett. 100 (2008) 070502 [arXiv:0704.3906].
J. Molina-Vilaplana and P. Sodano, Holographic view on quantum correlations and mutual information between disjoint blocks of a quantum critical system, JHEP 10 (2011) 011 [arXiv:1108.1277] [INSPIRE].
W. Fischler, A. Kundu and S. Kundu, Holographic mutual information at finite temperature, Phys. Rev. D 87 (2013) 126012 [arXiv:1212.4764] [INSPIRE].
H. Casini and M. Huerta, A finite entanglement entropy and the c-theorem, Phys. Lett. B 600 (2004) 142 [hep-th/0405111] [INSPIRE].
W. Fischler and S. Kundu, Strongly coupled gauge theories: high and low temperature behavior of non-local observables, JHEP 05 (2013) 098 [arXiv:1212.2643] [INSPIRE].
R.-G. Cai and N. Ohta, On the thermodynamics of large-N noncommutative super Yang-Mills theory, Phys. Rev. D 61 (2000) 124012 [hep-th/9910092] [INSPIRE].
D. Bigatti and L. Susskind, Magnetic fields, branes and noncommutative geometry, Phys. Rev. D 62 (2000) 066004 [hep-th/9908056] [INSPIRE].
L. Susskind, The quantum hall fluid and noncommutative Chern-Simons theory, hep-th/0101029 [INSPIRE].
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Fischler, W., Kundu, A. & Kundu, S. Holographic entanglement in a noncommutative gauge theory. J. High Energ. Phys. 2014, 137 (2014). https://doi.org/10.1007/JHEP01(2014)137
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DOI: https://doi.org/10.1007/JHEP01(2014)137