Abstract
We employ the free field realisation of the \( \mathfrak{psu}{\left(1,1\left|2\right.\right)}_1 \) world-sheet theory to constrain the correlators of string theory on AdS3 × S3 × 𝕋4 with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary S2 by the (genus zero) world-sheet — this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable ‘incidence relation’ obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.
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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].
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, Deriving the AdS3/CFT2 correspondence, JHEP 02 (2020) 136 [arXiv:1911.00378] [INSPIRE].
O. Lunin and S.D. Mathur, Correlation functions for MN/SN orbifolds, Commun. Math. Phys. 219 (2001) 399 [hep-th/0006196] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for symmetric product orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [INSPIRE].
L. Eberhardt, AdS3/CFT2 at higher genus, JHEP 05 (2020) 150 [arXiv:2002.11729] [INSPIRE].
Y. Hikida and T. Liu, Correlation functions of symmetric orbifold from AdS3 string theory, JHEP 09 (2020) 157 [arXiv:2005.12511] [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].
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].
N. Berkovits, An alternative string theory in twistor space for N = 4 super Yang-Mills, Phys. Rev. Lett. 93 (2004) 011601 [hep-th/0402045] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, work in progress.
K. Costello and N.M. Paquette, Twisted supergravity and Koszul duality: a case study in AdS3, arXiv:2001.02177 [INSPIRE].
S. Li and J. Troost, Twisted string theory in anti-de Sitter space, JHEP 11 (2020) 047 [arXiv:2005.13817] [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].
S. Ribault, Minisuperspace limit of the AdS3 WZNW model, JHEP 04 (2010) 096 [arXiv:0912.4481] [INSPIRE].
J. Teschner, The minisuperspace limit of the SL(2, C )/SU(2) WZNW model, Nucl. Phys. B 546 (1999) 369 [hep-th/9712258] [INSPIRE].
J. Teschner, Crossing symmetry in the \( {H}_3^{+} \) WZNW model, Phys. Lett. B 521 (2001) 127 [hep-th/0108121] [INSPIRE].
S. Ribault, Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory, JHEP 09 (2005) 045 [hep-th/0507114] [INSPIRE].
G. Giribet, On spectral flow symmetry and Knizhnik-Zamolodchikov equation, Phys. Lett. B 628 (2005) 148 [hep-th/0508019] [INSPIRE].
W.H. Baron and C.A. Núñez, Fusion rules and four-point functions in the SL(2, R) WZNW model, Phys. Rev. D 79 (2009) 086004 [arXiv:0810.2768] [INSPIRE].
F. Lesage, P. Mathieu, J. Rasmussen and H. Saleur, The \( \mathfrak{su}{(2)}_{-1/2} \) WZW model and the βγ system, Nucl. Phys. B 647 (2002) 363 [hep-th/0207201] [INSPIRE].
G. Götz, T. Quella and V. Schomerus, The WZNW model on PSU(1, 1|2), JHEP 03 (2007) 003 [hep-th/0610070] [INSPIRE].
D. Ridout, Fusion in fractional level \( \hat{sl}(2) \)-theories with k = − \( \frac{1}{2} \), Nucl. Phys. B 848 (2011) 216 [arXiv:1012.2905] [INSPIRE].
T. Quella and V. Schomerus, Superspace conformal field theory, J. Phys. A 46 (2013) 494010 [arXiv:1307.7724] [INSPIRE].
P. Goddard, Meromorphic conformal field theory, DAMTP-89-01, (1989) [INSPIRE].
M.R. Gaberdiel and P. Goddard, Axiomatic conformal field theory, Commun. Math. Phys. 209 (2000) 549 [hep-th/9810019] [INSPIRE].
S. Gerigk, String states on AdS3 × S3 from the supergroup, JHEP 10 (2012) 084 [arXiv:1208.0345] [INSPIRE].
N. Berkovits and C. Vafa, N = 4 topological strings, Nucl. Phys. B 433 (1995) 123 [hep-th/9407190] [INSPIRE].
K. Roumpedakis, Comments on the SN orbifold CFT in the large N -limit, JHEP 07 (2018) 038 [arXiv:1804.03207] [INSPIRE].
A. Dei and L. Eberhardt, Correlators of the symmetric product orbifold, JHEP 01 (2020) 108 [arXiv:1911.08485] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
R. Roiban, M. Spradlin and A. Volovich, On the tree level S matrix of Yang-Mills theory, Phys. Rev. D 70 (2004) 026009 [hep-th/0403190] [INSPIRE].
B. Knighton, Higher genus correlators for tensionless AdS3 strings, arXiv:2012.01445 [INSPIRE].
L. Eberhardt and M.R. Gaberdiel, Strings on AdS3 × S3 × S3 × S1, JHEP 06 (2019) 035 [arXiv:1904.01585] [INSPIRE].
L. Eberhardt, Partition functions of the tensionless string, arXiv:2008.07533 [INSPIRE].
S. Kawai and J.F. Wheater, Modular transformation and boundary states in logarithmic conformal field theory, Phys. Lett. B 508 (2001) 203 [hep-th/0103197] [INSPIRE].
M.R. Gaberdiel and I. Runkel, The logarithmic triplet theory with boundary, J. Phys. A 39 (2006) 14745 [hep-th/0608184] [INSPIRE].
T. Quella, V. Schomerus and T. Creutzig, Boundary spectra in superspace sigma-models, JHEP 10 (2008) 024 [arXiv:0712.3549] [INSPIRE].
V.G. Knizhnik and A.B. Zamolodchikov, Current algebra and Wess-Zumino model in two-dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].
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Dei, A., Gaberdiel, M.R., Gopakumar, R. et al. Free field world-sheet correlators for AdS3. J. High Energ. Phys. 2021, 81 (2021). https://doi.org/10.1007/JHEP02(2021)081
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DOI: https://doi.org/10.1007/JHEP02(2021)081