Abstract
The D1D5 CFT gives a holographic dual description of a near-extremal black hole in string theory. The interaction in this theory is given by a marginal deformation operator, which is composed of supercharges acting on a twist operator. The twist operator links together different copies of a free CFT. We study the effect of this deformation operator when it links together CFT copies with winding numbers M and N to produce a copy with winding M + N, populated with excitations of a particular form. We compute the effect of the deformation operator in the full supersymmetric theory, firstly on a Ramond-Ramond ground state and secondly on states with an initial bosonic or fermionic excitation. Our results generalize recent work which studied only the bosonic sector of the CFT. Our findings are a step towards understanding thermalization in the D1D5 CFT, which is related to black hole formation and evaporation in the bulk.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [INSPIRE].
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].
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].
R. Dijkgraaf, Instanton strings and hyper-Kähler geometry, Nucl. Phys. B 543 (1999) 545 [hep-th/9810210] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [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].
J.R. David, G. Mandal, S. Vaidya and S.R. Wadia, Point mass geometries, spectral flow and AdS 3 -CFT 2 correspondence, Nucl. Phys. B 564 (2000) 128 [hep-th/9906112] [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].
O. Lunin and S.D. Mathur, Rotating deformations of AdS 3 × S 3 , the orbifold CFT and strings in the pp wave limit, Nucl. Phys. B 642 (2002) 91 [hep-th/0206107] [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].
V. Balasubramanian, J. de Boer, E. Keski-Vakkuri and S.F. Ross, Supersymmetric conical defects: towards a string theoretic description of black hole formation, Phys. Rev. D 64 (2001) 064011 [hep-th/0011217] [INSPIRE].
J.M. Maldacena and L. Maoz, Desingularization by rotation, JHEP 12 (2002) 055 [hep-th/0012025] [INSPIRE].
O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].
O. Lunin, S.D. Mathur and A. Saxena, What is the gravity dual of a chiral primary?, Nucl. Phys. B 655 (2003) 185 [hep-th/0211292] [INSPIRE].
K. Skenderis and M. Taylor, Fuzzball solutions and D1-D5 microstates, Phys. Rev. Lett. 98 (2007) 071601 [hep-th/0609154] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Holographic anatomy of fuzzballs, JHEP 04 (2007) 023 [hep-th/0611171] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [INSPIRE].
O. Lunin, Adding momentum to D1-D5 system, JHEP 04 (2004) 054 [hep-th/0404006] [INSPIRE].
S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [INSPIRE].
S. Giusto, S.D. Mathur and A. Saxena, 3-charge geometries and their CFT duals, Nucl. Phys. B 710 (2005) 425 [hep-th/0406103] [INSPIRE].
S.D. Mathur and D. Turton, Microstates at the boundary of AdS, JHEP 05 (2012) 014 [arXiv:1112.6413] [INSPIRE].
S.D. Mathur and D. Turton, Momentum-carrying waves on D1-D5 microstate geometries, Nucl. Phys. B 862 (2012) 764 [arXiv:1202.6421] [INSPIRE].
O. Lunin, S.D. Mathur and D. Turton, Adding momentum to supersymmetric geometries, Nucl. Phys. B 868 (2013) 383 [arXiv:1208.1770] [INSPIRE].
S. Giusto and R. Russo, Superdescendants of the D1-D5 CFT and their dual 3-charge geometries, JHEP 03 (2014) 007 [arXiv:1311.5536] [INSPIRE].
V. Jejjala, O. Madden, S.F. Ross and G. Titchener, Non-supersymmetric smooth geometries and D1-D5-P bound states, Phys. Rev. D 71 (2005) 124030 [hep-th/0504181] [INSPIRE].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].
P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [INSPIRE].
S. Giusto, O. Lunin, S.D. Mathur and D. Turton, D1-D5-P microstates at the cap, JHEP 02 (2013) 050 [arXiv:1211.0306] [INSPIRE].
V. Cardoso, O.J.C. Dias, J.L. Hovdebo and R.C. Myers, Instability of non-supersymmetric smooth geometries, Phys. Rev. D 73 (2006) 064031 [hep-th/0512277] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Radiation from the non-extremal fuzzball, Class. Quant. Grav. 25 (2008) 135005 [arXiv:0711.4817] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Pair creation in non-extremal fuzzball geometries, Class. Quant. Grav. 25 (2008) 225021 [arXiv:0806.2309] [INSPIRE].
B.D. Chowdhury and S.D. Mathur, Non-extremal fuzzballs and ergoregion emission, Class. Quant. Grav. 26 (2009) 035006 [arXiv:0810.2951] [INSPIRE].
F.V. Dimitrakopoulos, B. Freivogel, M. Lippert and I.-S. Yang, Instability corners in AdS space, arXiv:1410.1880 [INSPIRE].
J. Berges, S. Borsányi and C. Wetterich, Prethermalization, Phys. Rev. Lett. 93 (2004) 142002 [hep-ph/0403234] [INSPIRE].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [INSPIRE].
S.G. Avery, B.D. Chowdhury and S.D. Mathur, Deforming the D1-D5 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 D1-D5 CFT, JHEP 06 (2010) 032 [arXiv:1003.2746] [INSPIRE].
Z. Carson, S. Hampton, S.D. Mathur and D. Turton, Effect of the twist operator in the D1-D5 CFT, JHEP 08 (2014) 064 [arXiv:1405.0259] [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].
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].
S.G. Avery and B.D. Chowdhury, Intertwining relations for the deformed D1-D5 CFT, JHEP 05 (2011) 025 [arXiv:1007.2202] [INSPIRE].
C.T. Asplund and S.G. Avery, Evolution of entanglement entropy in the D1-D5 brane system, Phys. Rev. D 84 (2011) 124053 [arXiv:1108.2510] [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. 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.A. Keller, Phase transitions in symmetric orbifold CFTs and universality, JHEP 03 (2011) 114 [arXiv:1101.4937] [INSPIRE].
C. Cardona, Pulsating strings from two dimensional CFT on (T 4)N /S(N), arXiv:1408.5035 [INSPIRE].
S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].
K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [INSPIRE].
V. Balasubramanian, J. de Boer, S. El-Showk and I. Messamah, Black holes as effective geometries, Class. Quant. Grav. 25 (2008) 214004 [arXiv:0811.0263] [INSPIRE].
B.D. Chowdhury and A. Virmani, Modave lectures on fuzzballs and emission from the D1-D5 system, arXiv:1001.1444 [INSPIRE].
S.D. Mathur, Black holes and beyond, Annals Phys. 327 (2012) 2760 [arXiv:1205.0776] [INSPIRE].
I. Bena and N.P. Warner, Resolving the structure of black holes: philosophizing with a hammer, arXiv:1311.4538 [INSPIRE].
I. Bena, J. de Boer, M. Shigemori and N.P. Warner, Double, double supertube bubble, JHEP 10 (2011) 116 [arXiv:1107.2650] [INSPIRE].
S. Giusto, R. Russo and D. Turton, New D1-D5-P geometries from string amplitudes, JHEP 11 (2011) 062 [arXiv:1108.6331] [INSPIRE].
G.W. Gibbons and N.P. Warner, Global structure of five-dimensional fuzzballs, Class. Quant. Grav. 31 (2014) 025016 [arXiv:1305.0957] [INSPIRE].
S.D. Mathur and D. Turton, Oscillating supertubes and neutral rotating black hole microstates, JHEP 04 (2014) 072 [arXiv:1310.1354] [INSPIRE].
I. Bena, S.F. Ross and N.P. Warner, On the oscillation of species, JHEP 09 (2014) 113 [arXiv:1312.3635] [INSPIRE].
I. Bena, M. Shigemori and N.P. Warner, Black-hole entropy from supergravity superstrata states, JHEP 10 (2014) 140 [arXiv:1406.4506] [INSPIRE].
F. Chen, B. Michel, J. Polchinski and A. Puhm, Journey to the center of the fuzzball, arXiv:1408.4798 [INSPIRE].
E.J. Martinec, The Cheshire cap, arXiv:1409.6017 [INSPIRE].
S.G. Avery, Using the D1-D5 CFT to understand black holes, arXiv:1012.0072 [INSPIRE].
S.G. Avery and B.D. Chowdhury, Emission from the D1-D5 CFT: higher twists, JHEP 01 (2010) 087 [arXiv:0907.1663] [INSPIRE].
D. Friedan, Introduction to Polyakov’s string theory, in Recent advances in field theory and statistical mechanics, J.B. Zuber and R. Stora eds., North Holland, The Netherlands (1984).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1410.4543
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Carson, Z., Hampton, S., Mathur, S.D. et al. Effect of the deformation operator in the D1D5 CFT. J. High Energ. Phys. 2015, 71 (2015). https://doi.org/10.1007/JHEP01(2015)071
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2015)071