Abstract
We continue our study of the worldsheet theory of superstrings on AdS3 × S3 × 𝕋4 in the tensionless limit [1]. We consider the theory on higher genus surfaces. We give evidence that the worldsheet correlators localise on certain worldsheets that cover the boundary of AdS3 holomorphically. This simplifies the string moduli space integral dramatically to a finite sum. This property shows that the higher genus corrections of the string worldsheet reproduce the structure of the 1/N corrections in the dual symmetric orbifold CFT SymN (𝕋4).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, Deriving the AdS3 /CFT2 correspondence, JHEP 02 (2020) 136 [arXiv:1911.00378] [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].
R. Gopakumar and C. Vafa, On the gauge theory/geometry correspondence, Adv. Theor. Math. Phys. 3 (1999) 1415 [hep-th/9811131] [INSPIRE].
D.J. Gross and A.A. Migdal, Nonperturbative Two-Dimensional Quantum Gravity, Phys. Rev. Lett. 64 (1990) 127 [INSPIRE].
M.R. Douglas and S.H. Shenker, Strings in Less Than One-Dimension, Nucl. Phys. B 335 (1990) 635 [INSPIRE].
P.M.S. Petropoulos, Comments on SU(1, 1) string theory, Phys. Lett. B 236 (1990) 151 [INSPIRE].
S. Hwang, No ghost theorem for SU(1, 1) string theories, Nucl. Phys. B 354 (1991) 100 [INSPIRE].
M. Henningson, S. Hwang, P. Roberts and B. Sundborg, Modular invariance of SU(1, 1) strings, Phys. Lett. B 267 (1991) 350 [INSPIRE].
J. Teschner, On structure constants and fusion rules in the SL(2, ℂ)/SU(2) WZNW model, Nucl. Phys. B 546 (1999) 390 [hep-th/9712256] [INSPIRE].
J.M. Evans, M.R. Gaberdiel and M.J. Perry, The no ghost theorem for AdS3 and the stringy exclusion principle, Nucl. Phys. B 535 (1998) 152 [hep-th/9806024] [INSPIRE].
J. Teschner, Operator product expansion and factorization in the \( {\mathrm{H}}_3^{+} \)WZNW model, Nucl. Phys. B 571 (2000) 555 [hep-th/9906215] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and SL(2, ℝ) WZW model 1.: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
J.M. Maldacena, H. Ooguri and J. Son, Strings in AdS3 and the SL(2, ℝ) WZW model. Part 2. Euclidean black hole, J. Math. Phys. 42 (2001) 2961 [hep-th/0005183] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and the SL(2, ℝ) WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006 [hep-th/0111180] [INSPIRE].
J. Teschner, Crossing symmetry in the \( {\mathrm{H}}_3^{+} \)WZNW model, Phys. Lett. B 521 (2001) 127 [hep-th/0108121] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS3 , JHEP 05 (2018) 085 [arXiv:1803.04423] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for Symmetric Product Orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [INSPIRE].
R. Gopakumar, From free fields to AdS, Phys. Rev. D 70 (2004) 025009 [hep-th/0308184] [INSPIRE].
R. Gopakumar, From free fields to AdS. 2., Phys. Rev. D 70 (2004) 025010 [hep-th/0402063] [INSPIRE].
R. Gopakumar, From free fields to AdS: III, Phys. Rev. D 72 (2005) 066008 [hep-th/0504229] [INSPIRE].
O. Aharony, J.R. David, R. Gopakumar, Z. Komargodski and S.S. Razamat, Comments on worldsheet theories dual to free large N gauge theories, Phys. Rev. D 75 (2007) 106006 [hep-th/0703141] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for M N /SN orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
O. Lunin and S.D. Mathur, Three point functions for M N /SN orbifolds with \( \mathcal{N} \) = 4 supersymmetry, Commun. Math. Phys. 227 (2002) 385 [hep-th/0103169] [INSPIRE].
A. Dei and L. Eberhardt, Correlators of the symmetric product orbifold, JHEP 01 (2020) 108 [arXiv:1911.08485] [INSPIRE].
A. Giveon, D. Kutasov and N. Seiberg, Comments on string theory on AdS3 , Adv. Theor. Math. Phys. 2 (1998) 733 [hep-th/9806194] [INSPIRE].
K. Ferreira, M.R. Gaberdiel and J.I. Jottar, Higher spins on AdS3 from the worldsheet, JHEP 07 (2017) 131 [arXiv:1704.08667] [INSPIRE].
L. Eberhardt and K. Ferreira, Long strings and chiral primaries in the hybrid formalism, JHEP 02 (2019) 098 [arXiv:1810.08621] [INSPIRE].
N. Berkovits, C. Vafa and E. Witten, Conformal field theory of AdS background with Ramond-Ramond flux, JHEP 03 (1999) 018 [hep-th/9902098] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, Virasoro amplitude from the SN 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 SN 8 supersymmetric orbifold σ-model, Nucl. Phys. B 524 (1998) 159 [hep-th/9712061] [INSPIRE].
A. Jevicki, M. Mihailescu and S. Ramgoolam, Gravity from CFT on SN (X ): Symmetries and interactions, Nucl. Phys. B 577 (2000) 47 [hep-th/9907144] [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].
K. Roumpedakis, Comments on the SN orbifold CFT in the large N -limit, JHEP 07 (2018) 038 [arXiv:1804.03207] [INSPIRE].
J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point, JHEP 01 (2017) 013 [arXiv:1509.03612] [INSPIRE].
P. Deligne et al. eds., Quantum fields and strings: A course for mathematicians. Vol. 1, 2, AMS (1999) [INSPIRE].
D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
A. Giveon, D. Kutasov, E. Rabinovici and A. Sever, Phases of quantum gravity in AdS3 and linear dilaton backgrounds, Nucl. Phys. B 719 (2005) 3 [hep-th/0503121] [INSPIRE].
G. Giribet, C. Hull, M. Kleban, M. Porrati and E. Rabinovici, Superstrings on AdS3 at k = 1, JHEP 08 (2018) 204 [arXiv:1803.04420] [INSPIRE].
V.G. Knizhnik and A.B. Zamolodchikov, Current Algebra and Wess-Zumino Model in Two-Dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].
J. de Boer, H. Ooguri, H. Robins and J. Tannenhauser, String theory on AdS3 , JHEP 12 (1998) 026 [hep-th/9812046] [INSPIRE].
A. Dei, L. Eberhardt and M.R. Gaberdiel, Three-point functions in AdS3 /CFT2 holography, JHEP 12 (2019) 012 [arXiv:1907.13144] [INSPIRE].
D. Friedan, Introduction to Polyakov’s String Theory, in Les Houches Summer School in Theoretical Physics: Recent Advances in Field Theory and Statistical Mechanics, Les Houches, France, 2 August–10 September 1982 [INSPIRE].
D. Bernard, On the Wess-Zumino-Witten Models on the Torus, Nucl. Phys. B 303 (1988) 77 [INSPIRE].
D. Bernard, On the Wess-Zumino-Witten Models on Riemann Surfaces, Nucl. Phys. B 309 (1988) 145 [INSPIRE].
S.D. Mathur, S. Mukhi and A. Sen, Correlators of Primary Fields in the SU(2) W Z W Theory on Riemann Surfaces, Nucl. Phys. B 305 (1988) 219 [INSPIRE].
S.D. Mathur, S. Mukhi and A. Sen, Differential Equations for Correlators and Characters in Arbitrary Rational Conformal Field Theories, Nucl. Phys. B 312 (1989) 15 [INSPIRE].
J.H. Bruinier, G. van der Geer, G. Harder and D. Zagier, The 1-2-3 of Modular Forms, Springer Science & Business Media (2008).
P.F. Stiller, Classical automorphic forms and hypergeometric functions, J. Number Theory 28 (1988) 219.
S.H. Shenker, The Strength of nonperturbative effects in string theory, in The Large N expansion in quantum field theory and statistical physics: From spin systems to two-dimensional gravity, pp. 191–200 (1990) [INSPIRE].
I. Aniceto, R. Schiappa and M. Vonk, The Resurgence of Instantons in String Theory, Commun. Num. Theor. Phys. 6 (2012) 339 [arXiv:1106.5922] [INSPIRE].
A. Dei, M.R. Gaberdiel and R. Gopakumar, in progress.
L. Rastelli and M. Wijnholt, Minimal AdS3 , Adv. Theor. Math. Phys. 11 (2007) 291 [hep-th/0507037] [INSPIRE].
K. Costello and N.M. Paquette, Twisted Supergravity and Koszul Duality: A case study in AdS3 , arXiv:2001.02177 [INSPIRE].
A. Okounkov and R. Pandharipande, Gromov-Witten Theory, Hurwitz Theory, and Completed Cycles, Annals Math. 163 (2006) 517.
J.D. Fay, Theta functions on Riemann surfaces, vol. 352, Springer (2006).
A. Erdélyi ed., Higher Transcendental Functions, vol. 2 of Bateman Manuscript Project, McGraw-Hill Book Company, New York (1953).
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
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2002.11729
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Eberhardt, L. AdS3/CFT2 at higher genus. J. High Energ. Phys. 2020, 150 (2020). https://doi.org/10.1007/JHEP05(2020)150
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2020)150