Abstract
Holography can provide a microscopic interpretation of a gravitational solution as corresponding to a particular CFT state: the asymptotic expansion in gravity encodes the expectation values of operators in the dual CFT state. Such a correspondence is particularly valuable in black hole physics. We study supersymmetric D1-D5-P black holes, for which recently constructed microstate solutions known as “superstrata” provide strong motivation to derive the explicit D1-D5 holographic dictionary for CFT operators of total dimension two. In this work we derive the explicit map between one-point functions of scalar chiral primaries of dimension (1, 1) and the asymptotic expansions of families of asymptotically AdS3 ×S3 × ℳ supergravity solutions, with ℳ either T4 or K3. We include all possible mixings between single-trace and multi-trace operators. We perform several tests of the holographic map, including new precision holographic tests of superstrata, that provide strong supporting evidence for the proposed dual CFT states.
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J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [Adv. Theor. Math. Phys.2 (1998) 231] [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].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev.D 14 (1976) 2460 [INSPIRE].
A.L. Fitzpatrick, J. Kaplan and M.T. Walters, Universality of Long-Distance AdS Physics from the CFT Bootstrap, JHEP08 (2014) 145 [arXiv:1403.6829] [INSPIRE].
T. Hartman, C.A. Keller and B. Stoica, Universal Spectrum of 2d Conformal Field Theory in the Large c Limit, JHEP09 (2014) 118 [arXiv:1405.5137] [INSPIRE].
T. Anous, T. Hartman, A. Rovai and J. Sonner, Black Hole Collapse in the 1/c Expansion, JHEP07 (2016) 123 [arXiv:1603.04856] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Li and J. Wang, On information loss in AdS 3/CFT 2, JHEP05 (2016) 109 [arXiv:1603.08925] [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, Using the D1D5 CFT to Understand Black Holes, Ph.D. Thesis, Ohio State University, Columbus U.S.A. (2010) [arXiv:1012.0072] [INSPIRE].
M. Baggio, J. de Boer and K. Papadodimas, A non-renormalization theorem for chiral primary 3-point functions, JHEP07 (2012) 137 [arXiv:1203.1036] [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, AdS/CFT duality and the black hole information paradox, Nucl. Phys.B 623 (2002) 342 [hep-th/0109154] [INSPIRE].
O. Lunin, J.M. Maldacena and L. Maoz, Gravity solutions for the D1-D5 system with angular momentum, hep-th/0212210 [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].
I. Bena and N.P. Warner, Resolving the Structure of Black Holes: Philosophizing with a Hammer, arXiv:1311.4538 [INSPIRE].
E.J. Martinec and S. Massai, String Theory of Supertubes, JHEP07 (2018) 163 [arXiv:1705.10844] [INSPIRE].
E.J. Martinec, S. Massai and D. Turton, String dynamics in NS5-F1-P geometries, JHEP09 (2018) 031 [arXiv:1803.08505] [INSPIRE].
N. Lashkari and J. Simón, From state distinguishability to effective bulk locality, JHEP06 (2014) 038 [arXiv:1402.4829] [INSPIRE].
S.D. Mathur and D. Turton, The fuzzball nature of two-charge black hole microstates, Nucl. Phys.B 945 (2019) 114684 [arXiv:1811.09647] [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, JHEP04 (2007) 023 [hep-th/0611171] [INSPIRE].
I. Kanitscheider, K. Skenderis and M. Taylor, Fuzzballs with internal excitations, JHEP06 (2007) 056 [arXiv:0704.0690] [INSPIRE].
M. Taylor, Matching of correlators in AdS 3/CFT 2, JHEP06 (2008) 010 [arXiv:0709.1838] [INSPIRE].
K. Skenderis and M. Taylor, Kaluza-Klein holography, JHEP05 (2006) 057 [hep-th/0603016] [INSPIRE].
M. Taylor, General 2 charge geometries, JHEP03 (2006) 009 [hep-th/0507223] [INSPIRE].
S. Giusto, E. Moscato and R. Russo, AdS 3holography for 1/4 and 1/8 BPS geometries, JHEP11 (2015) 004 [arXiv:1507.00945] [INSPIRE].
I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
I. Bena, E.J. Martinec, D. Turton and N.P. Warner, Momentum Fractionation on Superstrata, JHEP05 (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.J. Martinec, D. Turton and N.P. Warner, M-theory Superstrata and the MSW String, JHEP06 (2017) 137 [arXiv:1703.10171] [INSPIRE].
I. Bena, D. Turton, R. Walker and N.P. Warner, Integrability and Black-Hole Microstate Geometries, JHEP11 (2017) 021 [arXiv:1709.01107] [INSPIRE].
I. Bena et al., Asymptotically-flat supergravity solutions deep inside the black-hole regime, JHEP02 (2018) 014 [arXiv:1711.10474] [INSPIRE].
I. Bena, P. Heidmann and D. Turton, AdS 2holography: mind the cap, JHEP12 (2018) 028 [arXiv:1806.02834] [INSPIRE].
E. Bakhshaei and A. Bombini, Three-charge superstrata with internal excitations, Class. Quant. Grav.36 (2019) 055001 [arXiv:1811.00067] [INSPIRE].
I. Bena, E.J. Martinec, R. Walker and N.P. Warner, Early Scrambling and Capped BTZ Geometries, JHEP04 (2019) 126 [arXiv:1812.05110] [INSPIRE].
N. Čeplak, R. Russo and M. Shigemori, Supercharging Superstrata, JHEP03 (2019) 095 [arXiv:1812.08761] [INSPIRE].
P. Heidmann and N.P. Warner, Superstratum Symbiosis, arXiv:1903.07631 [INSPIRE].
S.D. Mathur and D. Turton, Microstates at the boundary of AdS, JHEP05 (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 D1D5 CFT and their dual 3-charge geometries, JHEP03 (2014) 007 [arXiv:1311.5536] [INSPIRE].
J. Garcia i Tormo and M. Taylor, One point functions for black hole microstates, arXiv:1904.10200 [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].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Extremal correlators in the AdS/CFT correspondence, hep-th/9908160 [INSPIRE].
G. Arutyunov and S. Frolov, On the correspondence between gravity fields and CFT operators, JHEP04 (2000) 017 [hep-th/0003038] [INSPIRE].
L. Rastelli and X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP04 (2018) 014 [arXiv:1710.05923] [INSPIRE].
J. Garcia i Tormo and M. Taylor, Correlation functions in the D1-D5 orbifold CFT, JHEP06 (2018) 012 [arXiv:1804.10205] [INSPIRE].
S. Giusto and R. Russo, Entanglement Entropy and D1-D5 geometries, Phys. Rev.D 90 (2014) 066004 [arXiv:1405.6185] [INSPIRE].
S. Ribault, Conformal field theory on the plane, arXiv:1406.4290 [INSPIRE].
O. Lunin and S.D. Mathur, Three point functions for M N/S Norbifolds with \( \mathcal{N} \) = 4 supersymmetry, Commun. Math. Phys.227 (2002) 385 [hep-th/0103169] [INSPIRE].
A. Tyukov, R. Walker and N.P. Warner, Tidal Stresses and Energy Gaps in Microstate Geometries, JHEP02 (2018) 122 [arXiv:1710.09006] [INSPIRE].
M. Bianchi, D. Consoli, A. Grillo and J.F. Morales, The dark side of fuzzball geometries, JHEP05 (2019) 126 [arXiv:1811.02397] [INSPIRE].
A. Bombini and A. Galliani, AdS 3four-point functions from \( \frac{1}{8} \)-BPS states, JHEP06 (2019) 044 [arXiv:1904.02656] [INSPIRE].
S.D. Mathur and D. Turton, Oscillating supertubes and neutral rotating black hole microstates, JHEP04 (2014) 072 [arXiv:1310.1354] [INSPIRE].
I. Bena, S.F. Ross and N.P. Warner, On the Oscillation of Species, JHEP09 (2014) 113 [arXiv:1312.3635] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for M N/S Norbifolds, Commun. Math. Phys.219 (2001) 399 [hep-th/0006196] [INSPIRE].
Z. Carson, S. Hampton, S.D. Mathur and D. Turton, Effect of the deformation operator in the D1D5 CFT, JHEP01 (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, JHEP08 (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].
S.G. Avery, B.D. Chowdhury and S.D. Mathur, Deforming the D1D5 CFT away from the orbifold point, JHEP06 (2010) 031 [arXiv:1002.3132] [INSPIRE].
B.A. Burrington, A.W. Peet and I.G. Zadeh, Twist-nontwist correlators in M N/S Norbifold 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, 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].
B.A. Burrington, I.T. Jardine and A.W. Peet, Operator mixing in deformed D1D5 CFT and the OPE on the cover, JHEP06 (2017) 149 [arXiv:1703.04744] [INSPIRE].
B.A. Burrington, I.T. Jardine and A.W. Peet, The OPE of bare twist operators in bosonic S Norbifold CFTs at large N, JHEP08 (2018) 202 [arXiv:1804.01562] [INSPIRE].
T. de Beer, B.A. Burrington, I.T. Jardine and A.W. Peet, The large N limit of OPEs in symmetric orbifold CFTs with \( \mathcal{N} \) = (4, 4) supersymmetry, arXiv:1904.07816 [INSPIRE].
S. Giusto, L. Martucci, M. Petrini and R. Russo, 6D microstate geometries from 10D structures, Nucl. Phys.B 876 (2013) 509 [arXiv:1306.1745] [INSPIRE].
S. Giusto, R. Russo and D. Turton, New D1-D5-P geometries from string amplitudes, JHEP11 (2011) 062 [arXiv:1108.6331] [INSPIRE].
I. Bena, S. Giusto, M. Shigemori and N.P. Warner, Supersymmetric Solutions in Six Dimensions: A Linear Structure, JHEP03 (2012) 084 [arXiv:1110.2781] [INSPIRE].
J.B. Gutowski, D. Martelli and H.S. Reall, All Supersymmetric solutions of minimal supergravity in six-dimensions, Class. Quant. Grav.20 (2003) 5049 [hep-th/0306235] [INSPIRE].
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Giusto, S., Rawash, S. & Turton, D. AdS3 holography at dimension two. J. High Energ. Phys. 2019, 171 (2019). https://doi.org/10.1007/JHEP07(2019)171
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DOI: https://doi.org/10.1007/JHEP07(2019)171