Abstract
Thermalization in the D1D5 CFT should occur via interactions caused by the twist operator, which deforms the theory off its free orbifold point. Earlier studies investigating this deformation at first order did not show any definite evidence of thermalization. In this paper we study the deformation to second order, where we do expect to see the effects that should give thermalization. We compute the effect of two twist operators on an initial vacuum state, which generates a squeezed state analogous to the case for a single twist. We obtain expressions for the Bogoliubov coefficients in this 2-twist case.
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References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for M N /S N orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
O. Lunin and S.D. Mathur, Three point functions for M N /S N orbifolds with N = 4 supersymmetry, Commun. Math. Phys. 227 (2002) 385 [hep-th/0103169] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, Virasoro amplitude from the S N R 24 orbifold σ-model, Theor. Math. Phys. 114 (1998) 43 [hep-th/9708129] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, Four graviton scattering amplitude from S N R 8 supersymmetric orbifold σ-model, Nucl. Phys. B 524 (1998) 159 [hep-th/9712061] [INSPIRE].
J. de Boer, Six-dimensional supergravity on S 3 × AdS 3 and 2D conformal field theory, Nucl. Phys. B 548 (1999) 139 [hep-th/9806104] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
R. Dijkgraaf, Instanton strings and hyperKähler geometry, Nucl. Phys. B 543 (1999) 545 [hep-th/9810210] [INSPIRE].
J.R. David, G. Mandal and S.R. Wadia, D1/D5 moduli in SCFT and gauge theory and Hawking radiation, Nucl. Phys. B 564 (2000) 103 [hep-th/9907075] [INSPIRE].
J. Gomis, L. Motl and A. Strominger, PP-wave/CFT 2 duality, JHEP 11 (2002) 016 [hep-th/0206166] [INSPIRE].
E. Gava and K.S. Narain, Proving the PP-wave/CFT 2 duality, JHEP 12 (2002) 023 [hep-th/0208081] [INSPIRE].
F. Larsen and E.J. Martinec, U(1) charges and moduli in the D1-D5 system, JHEP 06 (1999) 019 [hep-th/9905064] [INSPIRE].
A. Jevicki, M. Mihailescu and S. Ramgoolam, Gravity from CFT on S N (X): Symmetries and interactions, Nucl. Phys. B 577 (2000) 47 [hep-th/9907144] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for Symmetric Product Orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds, Phys. Rev. D 80 (2009) 086009 [arXiv:0905.3451] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, A Spin Chain for the Symmetric Product CFT(2), JHEP 05 (2010) 099 [arXiv:0912.0959] [INSPIRE].
C.G. Callan and J.M. Maldacena, D-brane approach to black hole quantum mechanics, Nucl. Phys. B 472 (1996) 591 [hep-th/9602043] [INSPIRE].
A. Dhar, G. Mandal and S.R. Wadia, Absorption versus decay of black holes in string theory and T symmetry, Phys. Lett. B 388 (1996) 51 [hep-th/9605234] [INSPIRE].
S.R. Das and S.D. Mathur, Comparing decay rates for black holes and D-branes, Nucl. Phys. B 478 (1996) 561 [hep-th/9606185] [INSPIRE].
S.R. Das and S.D. Mathur, Interactions involving D-branes, Nucl. Phys. B 482 (1996) 153 [hep-th/9607149] [INSPIRE].
J.M. Maldacena and A. Strominger, Black hole grey body factors and D-brane spectroscopy, Phys. Rev. D 55 (1997) 861 [hep-th/9609026] [INSPIRE].
S.G. Avery, B.D. Chowdhury and S.D. Mathur, Deforming the D1D5 CFT away from the orbifold point, JHEP 06 (2010) 031 [arXiv:1002.3132] [INSPIRE].
S.G. Avery, B.D. Chowdhury and S.D. Mathur, Excitations in the deformed D1D5 CFT, JHEP 06 (2010) 032 [arXiv:1003.2746] [INSPIRE].
B.A. Burrington, S.D. Mathur, A.W. Peet and I.G. Zadeh, Analyzing the squeezed state generated by a twist deformation, Phys. Rev. D 91 (2015) 124072 [arXiv:1410.5790] [INSPIRE].
Z. Carson, S.D. Mathur and D. Turton, Bogoliubov coefficients for the twist operator in the D1D5 CFT, Nucl. Phys. B 889 (2014) 443 [arXiv:1406.6977] [INSPIRE].
Z. Carson, S. Hampton, S.D. Mathur and D. Turton, Effect of the twist operator in the D1D5 CFT, JHEP 08 (2014) 064 [arXiv:1405.0259] [INSPIRE].
Z. Carson, S. Hampton, S.D. Mathur and D. Turton, Effect of the deformation operator in the D1D5 CFT, JHEP 01 (2015) 071 [arXiv:1410.4543] [INSPIRE].
B.A. Burrington, A.W. Peet and I.G. Zadeh, Twist-nontwist correlators in M N /S N orbifold CFTs, Phys. Rev. D 87 (2013) 106008 [arXiv:1211.6689] [INSPIRE].
B.A. Burrington, A.W. Peet and I.G. Zadeh, Operator mixing for string states in the D1-D5 CFT near the orbifold point, Phys. Rev. D 87 (2013) 106001 [arXiv:1211.6699] [INSPIRE].
A. Schwimmer and N. Seiberg, Comments on the N = 2, N = 3, N = 4 Superconformal Algebras in Two-Dimensions, Phys. Lett. B 184 (1987) 191 [INSPIRE].
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ArXiv ePrint: 1511.04046
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Carson, Z., Hampton, S. & Mathur, S.D. Second order effect of twist deformations in the D1D5 CFT. J. High Energ. Phys. 2016, 115 (2016). https://doi.org/10.1007/JHEP04(2016)115
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DOI: https://doi.org/10.1007/JHEP04(2016)115