Abstract
The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The radius of AdS3 is related to the level k of the WZNW model. For k = 3, our result should be an important ingredient for deriving AdS3/CFT2 correspondence with tensionless superstrings to all orders in string perturbation theory. For generic k, relations involving specific forms of correlation functions for strings on AdS3 × X were obtained.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.J. Gross, High-energy symmetries of string theory, Phys. Rev. Lett. 60 (1988) 1229 [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].
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].
A. Dei, L. Eberhardt and M.R. Gaberdiel, Three-point functions in AdS3 /CFT2 holography, JHEP 12 (2019) 012 [arXiv:1907.13144] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and R. Gopakumar, Deriving the AdS3 /CFT2 correspondence, JHEP 02 (2020) 136 [arXiv:1911.00378] [INSPIRE].
A. Dei and L. Eberhardt, Correlators of the symmetric product orbifold, JHEP 01 (2020) 108 [arXiv:1911.08485] [INSPIRE].
L. Eberhardt, AdS3 /CFT2 at higher genus, JHEP 05 (2020) 150 [arXiv:2002.11729] [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 N = 4 supersymmetry, Commun. Math. Phys. 227 (2002) 385 [hep-th/0103169] [INSPIRE].
Y. Hikida and V. Schomerus, \( {H}_3^{+} \) WZNW model from Liouville field theory, JHEP 10 (2007) 064 [arXiv:0706.1030] [INSPIRE].
Y. Hikida and V. Schomerus, The FZZ-duality conjecture: a proof, JHEP 03 (2009) 095 [arXiv:0805.3931] [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].
J. de Boer, H. Ooguri, H. Robins and J. Tannenhauser, String theory on AdS3 , JHEP 12 (1998) 026 [hep-th/9812046] [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 SL(2, R) WZW model. Part 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].
G. Giribet and C.A. Nún˜ez, Correlators in AdS3 string theory, JHEP 06 (2001) 010 [hep-th/0105200] [INSPIRE].
S. Ribault, Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory, JHEP 09 (2005) 045 [hep-th/0507114] [INSPIRE].
G. Giribet, A. Pakman and L. Rastelli, Spectral flow in AdS3 /CFT2 , JHEP 06 (2008) 013 [arXiv:0712.3046] [INSPIRE].
S. Ribault and J. Teschner, \( {H}_3^{+} \) -WZNW correlators from Liouville theory, JHEP 06 (2005) 014 [hep-th/0502048] [INSPIRE].
Y. Hikida and V. Schomerus, Structure constants of the OSP(1|2) WZNW model, JHEP 12 (2007) 100 [arXiv:0711.0338] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Supergroup — extended super Liouville correspondence, JHEP 06 (2011) 063 [arXiv:1103.5753] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Correspondences between WZNW models and CFTs with W -algebra symmetry, JHEP 02 (2016) 048 [arXiv:1509.07516] [INSPIRE].
T. Creutzig, N. Genra, Y. Hikida and T. Liu, Correspondences among CFTs with different W -algebra symmetry, Nucl. Phys. B 957 (2020) 115104 [arXiv:2002.12587] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for symmetric product orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and C. Hull, Stringy AdS3 from the worldsheet, JHEP 07 (2017) 090 [arXiv:1704.08665] [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].
D. Friedan, Introduction to Polyakov’s string theory, in Les Houches summer school in theoretical physics: recent advances in field theory and statistical mechanics, (1982) [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Structure constants and conformal bootstrap in Liouville field theory, Nucl. Phys. B 477 (1996) 577 [hep-th/9506136] [INSPIRE].
A.M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].
K. Roumpedakis, Comments on the SN orbifold CFT in the large N -limit, JHEP 07 (2018) 038 [arXiv:1804.03207] [INSPIRE].
M. Wakimoto, Fock representations of the affine Lie algebra \( {A}_1^1 \), Commun. Math. Phys. 104 (1986) 605 [INSPIRE].
R. Argurio, A. Giveon and A. Shomer, Superstrings on AdS3 and symmetric products, JHEP 12 (2000) 003 [hep-th/0009242] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Chiral bosonization, determinants and the string partition function, Nucl. Phys. B 288 (1987) 357 [INSPIRE].
J.D. Fay, Theta functions on Riemann surfaces, Springer, Berlin, Heidelberg, Germany (1973).
D. Mumford, Tata lectures on theta I, Birkhäuser, Boston, Ma, U.S.A. (1983).
L. Álvarez-Gaumé, G.W. Moore and C. Vafa, Theta functions, modular invariance and strings, Commun. Math. Phys. 106 (1986) 1 [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].
M.R. Gaberdiel and R. Gopakumar, Large N = 4 holography, JHEP 09 (2013) 036 [arXiv:1305.4181] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Higher spins & strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Higher spin AdS3 supergravity and its dual CFT, JHEP 02 (2012) 109 [arXiv:1111.2139] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Extended higher spin holography and Grassmannian models, JHEP 11 (2013) 038 [arXiv:1306.0466] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Rønne, Higher spin AdS3 holography with extended supersymmetry, JHEP 10 (2014) 163 [arXiv:1406.1521] [INSPIRE].
M.A. Vasiliev, From Coxeter higher-spin theories to strings and tensor models, JHEP 08 (2018) 051 [arXiv:1804.06520] [INSPIRE].
R. Argurio, A. Giveon and A. Shomer, Superstring theory on AdS3 × G/H and boundary N = 3 superconformal symmetry, JHEP 04 (2000) 010 [hep-th/0002104] [INSPIRE].
R. Argurio, A. Giveon and A. Shomer, The spectrum of N = 3 string theory on AdS3 × G/H , JHEP 12 (2000) 025 [hep-th/0011046] [INSPIRE].
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: 2005.12511
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
Hikida, Y., Liu, T. Correlation functions of symmetric orbifold from AdS3 string theory. J. High Energ. Phys. 2020, 157 (2020). https://doi.org/10.1007/JHEP09(2020)157
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2020)157