Abstract
The D1-D5 system has an orbifold point in its moduli space, at which it may be described by an \( \mathcal{N} \) = (4,4) supersymmetric sigma model with target space MN /S(N) where M is \( {\mathbb{T}}^4 \) or K3. In this paper we consider correlation functions involving chiral operators constructed from twist fields: we find explicit expressions for processes involving a twist n operator joining n twist operators of arbitrary twist. These expressions are universal, in that they are independent of the choice of M , and the final results can be expressed in a compact form. We explain how these results are relevant to the black hole microstate programme: one point functions of chiral operators can be used to reconstruct AdS3 near horizon regions of D1-D5 microstates and to match microstates constructed in supergravity with the CFT.
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].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [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 and S.D. Mathur, Metric of the multiply wound rotating string, Nucl. Phys. B 610 (2001) 49 [hep-th/0105136] [INSPIRE].
O. Lunin and S.D. Mathur, Statistical interpretation of Bekenstein entropy for systems with a stretched horizon, Phys. Rev. Lett. 88 (2002) 211303 [hep-th/0202072] [INSPIRE].
S.D. Mathur, A proposal to resolve the black hole information paradox, Int. J. Mod. Phys. D 11 (2002) 1537 [hep-th/0205192] [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].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216].
K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [INSPIRE].
S.D. Mathur, What Exactly is the Information Paradox?, Lect. Notes Phys. 769 (2009) 3 [arXiv:0803.2030].
M. Shigemori, Exotic branes and black hole microstates, Int. J. Mod. Phys. Conf. Ser. 21 (2013) 77 [INSPIRE].
O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [INSPIRE].
M. Taylor, General 2 charge geometries, JHEP 03 (2006) 009 [hep-th/0507223] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP 06 (2007) 056 [arXiv:0704.0690] [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].
S.D. Mathur, A. Saxena and Y.K. Srivastava, Constructing ‘hair’ for the three charge hole, Nucl. Phys. B 680 (2004) 415 [hep-th/0311092] [INSPIRE].
I. Bena and P. Kraus, Microscopic description of black rings in AdS/CFT, JHEP 12 (2004) 070 [hep-th/0408186] [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].
O. Lunin, Adding momentum to D1-D5 system, JHEP 04 (2004) 054 [hep-th/0404006] [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].
V. Balasubramanian, P. Kraus and M. Shigemori, Massless black holes and black rings as effective geometries of the D1-D5 system, Class. Quant. Grav. 22 (2005) 4803 [hep-th/0508110] [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].
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].
S. Giusto and R. Russo, Adding new hair to the 3-charge black ring, Class. Quant. Grav. 29 (2012) 085006 [arXiv:1201.2585] [INSPIRE].
S. Giusto and R. Russo, Perturbative superstrata, Nucl. Phys. B 869 (2013) 164 [arXiv:1211.1957] [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].
S. Giusto and R. Russo, Superdescendants of the D1D5 CFT and their dual 3-charge geometries, JHEP 03 (2014) 007 [arXiv:1311.5536] [INSPIRE].
I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
B. Chakrabarty, D. Turton and A. Virmani, Holographic description of non-supersymmetric orbifolded D1-D5-P solutions, JHEP 11 (2015) 063 [arXiv:1508.01231] [INSPIRE].
S. Giusto, E. Moscato and R. Russo, AdS 3 holography for 1/4 and 1/8 BPS geometries, JHEP 11 (2015) 004 [arXiv:1507.00945] [INSPIRE].
I. Bena, E. Martinec, D. Turton and N.P. Warner, Momentum Fractionation on Superstrata, JHEP 05 (2016) 064 [arXiv:1601.05805] [INSPIRE].
I. Bena et al., Smooth horizonless geometries deep inside the black-hole regime, Phys. Rev. Lett. 117 (2016) 201601 [arXiv:1607.03908] [INSPIRE].
I. Bena, E. Martinec, D. Turton and N.P. Warner, M-theory Superstrata and the MSW String, JHEP 06 (2017) 137 [arXiv:1703.10171] [INSPIRE].
E.J. Martinec and S. Massai, String Theory of Supertubes, arXiv:1705.10844 [INSPIRE].
A. Bombini and S. Giusto, Non-extremal superdescendants of the D1D5 CFT, JHEP 10 (2017) 023 [arXiv:1706.09761] [INSPIRE].
I. Bena, D. Turton, R. Walker and N.P. Warner, Integrability and Black-Hole Microstate Geometries, JHEP 11 (2017) 021 [arXiv:1709.01107] [INSPIRE].
I. Bena, P. Heidmann and P.F. Ramirez, A systematic construction of microstate geometries with low angular momentum, JHEP 10 (2017) 217 [arXiv:1709.02812] [INSPIRE].
I. Bena et al., Asymptotically-flat supergravity solutions deep inside the black-hole regime, JHEP 02 (2018) 014 [arXiv:1711.10474] [INSPIRE].
G. Bossard, S. Katmadas and D. Turton, Two Kissing Bolts, JHEP 02 (2018) 008 [arXiv:1711.04784] [INSPIRE].
K. Skenderis and M. Taylor, Kaluza-Klein holography, JHEP 05 (2006) 057 [hep-th/0603016] [INSPIRE].
A. Galliani, S. Giusto and R. Russo, Holographic 4-point correlators with heavy states, JHEP 10 (2017) 040 [arXiv:1705.09250] [INSPIRE].
A. Bombini, A. Galliani, S. Giusto, E. Moscato and R. Russo, Unitary 4-point correlators from classical geometries, Eur. Phys. J. C 78 (2018) 8 [arXiv:1710.06820] [INSPIRE].
K. Skenderis and M. Taylor, Holographic Coulomb branch vevs, JHEP 08 (2006) 001 [hep-th/0604169] [INSPIRE].
A. Pakman and A. Sever, Exact N = 4 correlators of AdS 3 /CF T 2, Phys. Lett. B 652 (2007) 60 [arXiv:0704.3040] [INSPIRE].
A. Dabholkar and A. Pakman, Exact chiral ring of AdS 3 /CF T 2, Adv. Theor. Math. Phys. 13 (2009) 409 [hep-th/0703022] [INSPIRE].
M.R. Gaberdiel and I. Kirsch, Worldsheet correlators in AdS 3 /CF T 2, JHEP 04 (2007) 050 [hep-th/0703001] [INSPIRE].
M. Taylor, Matching of correlators in AdS 3 /CF T 2, JHEP 06 (2008) 010 [arXiv:0709.1838] [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, Emission from the D1D5 CFT: Higher Twists, JHEP 01 (2010) 087 [arXiv:0907.1663] [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 and B.D. Chowdhury, Intertwining Relations for the Deformed D1D5 CFT, JHEP 05 (2011) 025 [arXiv:1007.2202] [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, 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].
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. Hampton, S.D. Mathur and D. Turton, Effect of the deformation operator in the D1D5 CFT, JHEP 01 (2015) 071 [arXiv:1410.4543] [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].
B.A. Burrington, A.W. Peet and I.G. Zadeh, Bosonization, cocycles and the D1-D5 CFT on the covering surface, Phys. Rev. D 93 (2016) 026004 [arXiv:1509.00022] [INSPIRE].
Z. Carson, S. Hampton and S.D. Mathur, Second order effect of twist deformations in the D1D5 CFT, JHEP 04 (2016) 115 [arXiv:1511.04046] [INSPIRE].
Z. Carson, S. Hampton and S.D. Mathur, Full action of two deformation operators in the D1D5 CFT, JHEP 11 (2017) 096 [arXiv:1612.03886] [INSPIRE].
B.A. Burrington, I.T. Jardine and A.W. Peet, Operator mixing in deformed D1D5 CFT and the OPE on the cover, JHEP 06 (2017) 149 [arXiv:1703.04744] [INSPIRE].
Z. Carson, I.T. Jardine and A.W. Peet, Component twist method for higher twists in D1-D5 CFT, Phys. Rev. D 96 (2017) 026006 [arXiv:1704.03401] [INSPIRE].
B.A. Burrington, I.T. Jardine and A.W. Peet, The OPE of bare twist operators in bosonic S N orbifold CFTs at large N , arXiv:1804.01562 [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].
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].
H.J. Boonstra, B. Peeters and K. Skenderis, Duality and asymptotic geometries, Phys. Lett. B 411 (1997) 59 [hep-th/9706192] [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].
J.M. Maldacena and L. Susskind, D-branes and fat black holes, Nucl. Phys. B 475 (1996) 679 [hep-th/9604042] [INSPIRE].
S. Deger, A. Kaya, E. Sezgin and P. Sundell, Spectrum of D = 6, N=4b supergravity on AdS in three-dimensions ×S 3, Nucl. Phys. B 536 (1998) 110 [hep-th/9804166] [INSPIRE].
G. Arutyunov, A. Pankiewicz and S. Theisen, Cubic couplings in D = 6 N = 4b supergravity on AdS 3 × S 3, Phys. Rev. D 63 (2001) 044024 [hep-th/0007061] [INSPIRE].
J. de Boer, A. Pasquinucci and K. Skenderis, AdS/CFT dualities involving large 2-D N = 4 superconformal symmetry, Adv. Theor. Math. Phys. 3 (1999) 577 [hep-th/9904073] [INSPIRE].
S. Gukov, E. Martinec, G.W. Moore and A. Strominger, The search for a holographic dual to AdS 3 × S 3 × S 3 × S 1, Adv. Theor. Math. Phys. 9 (2005) 435 [hep-th/0403090] [INSPIRE].
M.R. Gaberdiel and M. Kelm, The symmetric orbifold of \( \mathcal{N} \) = 2 minimal models, JHEP 07 (2016) 113 [arXiv:1604.03964] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel, R. Gopakumar and W. Li, BPS spectrum on AdS 3 × S 3 × S 3 × S 1, JHEP 03 (2017) 124 [arXiv:1701.03552] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and W. Li, A holographic dual for string theory on AdS 3 × S 3 × S 3 × S 1, JHEP 08 (2017) 111 [arXiv:1707.02705] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and C. Hull, Stringy AdS 3 from the worldsheet, JHEP 07 (2017) 090 [arXiv:1704.08665] [INSPIRE].
M. Baggio, O. Ohlsson Sax, A. Sfondrini, B. Stefanski and A. Torrielli, Protected string spectrum in AdS 3 /CFT 2 from worldsheet integrability, JHEP 04 (2017) 091 [arXiv:1701.03501] [INSPIRE].
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: 1804.10205
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
i Tormo, J.G., Taylor, M. Correlation functions in the D1-D5 orbifold CFT. J. High Energ. Phys. 2018, 12 (2018). https://doi.org/10.1007/JHEP06(2018)012
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)012