Abstract
The BPS correlators of the symmetric product orbifold SymN(𝕋4) are reproduced from the dual worldsheet theory describing strings on AdS3 × S3 × 𝕋4 with minimal (k = 1) NS-NS flux. More specifically, we show that the worldsheet duals of the symmetric orbifold BPS states can be identified with their lift to the covering surface, thereby making the matching of the correlators essentially manifest. We also argue that the argument can be generalised to arbitrary descendants, using suitable DDF operators on the worldsheet.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, Deriving the AdS3/CFT2 correspondence, JHEP 02 (2020) 136 [arXiv:1911.00378] [INSPIRE].
A. Dei, M.R. Gaberdiel, R. Gopakumar and B. Knighton, Free field world-sheet correlators for AdS3, JHEP 02 (2021) 081 [arXiv:2009.11306] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for MN/SN orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
O. Lunin and S.D. Mathur, Three point functions for MN/SN orbifolds with N = 4 supersymmetry, Commun. Math. Phys. 227 (2002) 385 [hep-th/0103169] [INSPIRE].
L. Eberhardt, AdS3/CFT2 at higher genus, JHEP 05 (2020) 150 [arXiv:2002.11729] [INSPIRE].
B. Knighton, Higher genus correlators for tensionless AdS3 strings, JHEP 04 (2021) 211 [arXiv:2012.01445] [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].
M.R. Gaberdiel and K. Naderi, The physical states of the Hybrid Formalism, JHEP 10 (2021) 168 [arXiv:2106.06476] [INSPIRE].
L. Eberhardt and M.R. Gaberdiel, String theory on AdS3 and the symmetric orbifold of Liouville theory, Nucl. Phys. B 948 (2019) 114774 [arXiv:1903.00421] [INSPIRE].
K. Naderi, DDF operators in the Hybrid Formalism, arXiv:2208.01617 [INSPIRE].
K. Roumpedakis, Comments on the SN orbifold CFT in the large N-limit, JHEP 07 (2018) 038 [arXiv:1804.03207] [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].
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].
M. Henningson, S. Hwang, P. Roberts and B. Sundborg, Modular invariance of SU(1, 1) strings, Phys. Lett. B 267 (1991) 350 [INSPIRE].
M.R. Gaberdiel, K. Naderi and V. Sriprachyakul, The free field realisation of the BVW string, JHEP 08 (2022) 274 [arXiv:2202.11392] [INSPIRE].
S. Gerigk, String States on AdS3 × S3 from the Supergroup, JHEP 10 (2012) 084 [arXiv:1208.0345] [INSPIRE].
D. Kutasov and N. Seiberg, More comments on string theory on AdS3, JHEP 04 (1999) 008 [hep-th/9903219] [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].
A. Dei and L. Eberhardt, Correlators of the symmetric product orbifold, JHEP 01 (2020) 108 [arXiv:1911.08485] [INSPIRE].
A. Dei and L. Eberhardt, String correlators on AdS3: three-point functions, JHEP 08 (2021) 025 [arXiv:2105.12130] [INSPIRE].
A. Dei and L. Eberhardt, String correlators on AdS3: four-point functions, JHEP 09 (2021) 209 [arXiv:2107.01481] [INSPIRE].
A. Dei and L. Eberhardt, String correlators on AdS3: Analytic structure and dual CFT, SciPost Phys. 13 (2022) 053 [arXiv:2203.13264] [INSPIRE].
E. Del Giudice, P. Di Vecchia and S. Fubini, General properties of the dual resonance model, Annals Phys. 70 (1972) 378 [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].
M. Wakimoto, Fock representations of the affine lie algebra \( {A}_1^{(1)} \), Commun. Math. Phys. 104 (1986) 605 [INSPIRE].
G. Giribet and C.A. Núñez, Aspects of the free field description of string theory on AdS3, JHEP 06 (2000) 033 [hep-th/0006070] [INSPIRE].
K. Hosomichi, K. Okuyama and Y. Satoh, Free field approach to string theory on AdS3, Nucl. Phys. B 598 (2001) 451 [hep-th/0009107] [INSPIRE].
P. Goddard, Meromorphic CFT, in Infinite dimensional Lie algebras and Lie groups, V.G. Kac ed., World Scientific (1989), p. 556.
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: 2207.03956
Rights and permissions
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.
About this article
Cite this article
Gaberdiel, M.R., Nairz, B. BPS correlators for AdS3/CFT2. J. High Energ. Phys. 2022, 244 (2022). https://doi.org/10.1007/JHEP09(2022)244
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2022)244