Abstract
Noncommutative deformations of the BTZ black holes are described by non- commutative cylinders. We study the scalar fields in this background. The spectrum is studied analytically and through numerical simulations we establish the existence of novel ‘stripe phases’. These are different from stripes on Moyal spaces and stable due to topo- logical obstruction.
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S. Doplicher, K. Fredenhagen and J.E. Roberts, The quantum structure of space-time at the Planck scale and quantum fields, Commun. Math. Phys. 172 (1995) 187 [hep-th/0303037] [INSPIRE].
P. Aschieri, C. Blohmann, M. Dimitrijevíc, F. Meyer, P. Schupp, et al., A gravity theory on noncommutative spaces, Class. Quant. Grav. 22 (2005) 3511 [hep-th/0504183] [INSPIRE].
A.P. Balachandran, T.R. Govindarajan, K.S. Gupta and S. Kurkcuoglu, Noncommutative two dimensional gravities, Class. Quant. Grav. 23 (2006) 5799 [hep-th/0602265] [INSPIRE].
B. Dolan, K.S. Gupta and A. Stern, Noncommutative BTZ black hole and discrete time, Class. Quant. Grav. 24 (2007) 1647 [hep-th/0611233] [INSPIRE].
P. Schupp and S. Solodukhin, Exact black hole solutions in noncommutative gravity, arXiv:0906.2724 [INSPIRE].
T. Ohl and A. Schenkel, Cosmological and black hole spacetimes in twisted noncommutative gravity, JHEP 10 (2009) 052 [arXiv:0906.2730] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [gr-qc/9302012] [INSPIRE].
H. Grosse and P. Prešnajder, Elements of a field theory on a noncommutative cylinder, Acta Phys. Slov. 49 (1999) 185 [INSPIRE].
J. Lukierski, H. Ruegg, A. Nowicki and V.N. Tolstoi, Q deformation of Poincar´e algebra, Phys. Lett. B 264 (1991) 331 [INSPIRE].
J. Lukierski, H. Ruegg and W.J. Zakrzewski, Classical quantum mechanics of free κ relativistic systems, Annals Phys. 243 (1995) 90 [hep-th/9312153] [INSPIRE].
S. Meljanac and M. Stojic, New realizations of Lie algebra κ-deformed Euclidean space, Eur. Phys. J. C 47 (2006) 531 [hep-th/0605133] [INSPIRE].
S. Meljanac, A. Samsarov, M. Stojic and K.S. Gupta, κ-Minkowski space-time and the star product realizations, Eur. Phys. J. C 53 (2008) 295 [arXiv:0705.2471] [INSPIRE].
M. Daszkiewicz, J. Lukierski and M. Woronowicz, κ-deformed oscillators, the choice of star product and free κ-deformed quantum fields, J. Phys. A A 42 (2009) 355201 [arXiv:0807.1992] [INSPIRE].
J. Lukierski, κ-deformed oscillators: deformed multiplication versus deformed flip operator and multiparticle clusters, Rept. Math. Phys. 64 (2009) 299 [arXiv:0812.0547] [INSPIRE].
T.R. Govindarajan, K.S. Gupta, E. Harikumar, S. Meljanac and D. Meljanac, Twisted statistics in κ-Minkowski spacetime, Phys. Rev. D 77 (2008) 105010 [arXiv:0802.1576] [INSPIRE].
T.R. Govindarajan, K.S. Gupta, E. Harikumar, S. Meljanac and D. Meljanac, Deformed oscillator algebras and QFT in κ-Minkowski spacetime, Phys. Rev. D 80 (2009) 025014 [arXiv:0903.2355] [INSPIRE].
T.R. Govindarajan, K.S. Gupta, E. Harikumar and S. Meljanac, Noncommutative geometry, symmetries and quantum structure of space-time, J. Phys. Conf. Ser. 306 (2011) 012019 [INSPIRE].
K.S. Gupta, S. Meljanac and A. Samsarov, Quantum statistics and noncommutative black holes, arXiv:1108.0341 [INSPIRE].
M. Chaichian, A. Demichev, P. Prešnajder and A. Tureanu, Noncommutative quantum field theory: unitarity and discrete time, Phys. Lett. B 515 (2001) 426 [INSPIRE].
A.P. Balachandran, T.R. Govindarajan, A. Martins and P. Teotonio-Sobrinho, Time-space noncommutativity: quantised evolutions, JHEP 11 (2004) 068 [hep-th/0410067] [INSPIRE].
J. Madore, An introduction to noncommutative differential geometry and its physical applications, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge U.K. (1999).
A.P. Balachandran, S. Kurkcuoglu and S. Vaidya, Lectures on fuzzy and fuzzy SUSY physics, World Scientific, Singapore (2007).
J. Hoppe, Quantum theory of a massless relativistic surface and a two dimensional bound state problem, Ph.D. Thesis, MIT, Cambridge U.S.A. (1982).
A.P. Balachandran, T.R. Govindarajan and B. Ydri, The fermion doubling problem and noncommutative geometry, Mod. Phys. Lett. A 15 (2000) 1279 [hep-th/9911087] [INSPIRE].
A.P. Balachandran, A. Pinzul and B.A. Qureshi, SUSY anomalies break N = 2 to N = 1: the supersphere and the fuzzy supersphere, JHEP 12 (2005) 002 [hep-th/0506037] [INSPIRE].
S.S. Gubser and S.L. Sondhi, Phase structure of noncommutative scalar field theories, Nucl. Phys. B 605 (2001) 395 [hep-th/0006119] [INSPIRE].
X. Martin, A matrix phase for the φ4 scalar field on the fuzzy sphere, JHEP 04 (2004) 077 [hep-th/0402230] [INSPIRE].
J. Medina, W. Bietenholz, F. Hofheinz and D. O’Connor, Field theory simulations on a fuzzy sphere: an alternative to the lattice, PoS LAT2005 (2006) 263 [hep-lat/0509162] [INSPIRE].
F. Garcia Flores, D. O’Connor and X. Martin, Simulating the scalar field on the fuzzy sphere, PoS LAT2005 (2006) 262 [hep-lat/0601012] [INSPIRE].
D. O’Connor and B. Ydri, Monte Carlo simulation of a NC gauge theory on the fuzzy sphere, JHEP 11 (2006) 016 [hep-lat/0606013] [INSPIRE].
J. Medina, Fuzzy scalar field theories: numerical and analytical investigations, arXiv:0801.1284 [INSPIRE].
W. Bietenholz, F. Hofheinz and J. Nishimura, The noncommutative λφ4 model, Acta Phys. Polon. B 34 (2003) 4711 [hep-th/0309216] [INSPIRE].
W. Bietenholz, F. Hofheinz and J. Nishimura, Numerical results on the noncommutative λφ4 model, Nucl. Phys. Proc. Suppl. 129 (2004) 865 [hep-th/0309182] [INSPIRE].
M. Panero, Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere, SIGMA 2 (2006) 081 [hep-th/0609205] [INSPIRE].
C. Das, S. Digal and T.R. Govindarajan, Finite temperature phase transition of a single scalar field on a fuzzy sphere, Mod. Phys. Lett. A 23 (2008) 1781 [arXiv:0706.0695] [INSPIRE].
C. Das, S. Digal and T.R. Govindarajan, Spontaneous symmetry breakdown in fuzzy spheres, Mod. Phys. Lett. A 24 (2009) 2693 [arXiv:0801.4479] [INSPIRE].
J. Ambjørn and S. Catterall, Stripes from (noncommutative) stars, Phys. Lett. B 549 (2002) 253 [hep-lat/0209106] [INSPIRE].
J. Medina, W. Bietenholz and D. O’Connor, Probing the fuzzy sphere regularisation in simulations of the 3D λφ4 model, JHEP 04 (2008) 041 [arXiv:0712.3366] [INSPIRE].
D. O’Connor, private communication.
S. Digal and T.R. Govindarajan, Topological stability of broken symmetry on fuzzy spheres, arXiv:1108.3320 [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
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Digal, S., Govindarajan, T.R., Gupta, K.S. et al. Phase structure of fuzzy black holes. J. High Energ. Phys. 2012, 27 (2012). https://doi.org/10.1007/JHEP01(2012)027
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DOI: https://doi.org/10.1007/JHEP01(2012)027