Abstract
In a recent letter we presented the equations which describe tensionless limit of the excited-state spectrum for strings on AdS3 × S3 × T4 supported by Ramond-Ramond flux, and their numerical solution. In this paper, we give a detailed account of the derivation of these equations from the mirror TBA equations proposed by Frolov and Sfondrini, discussing the contour-deformation trick which we used to obtain excited-state equations and the tensionless limit. We also comment at length on the algorithm for the numerical solution of the equations in the tensionless limit, and present a number of explicit numerical results, as well as comment on their interpretation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
A.S. Haupt, S. Lautz and G. Papadopoulos, A non-existence theorem for N > 16 supersymmetric AdS3 backgrounds, JHEP 07 (2018) 178 [arXiv:1803.08428] [INSPIRE].
F. Larsen and E.J. Martinec, U(1) charges and moduli in the D1 - D5 system, JHEP 06 (1999) 019 [hep-th/9905064] [INSPIRE].
O. Ohlsson Sax and B. Stefański, Closed strings and moduli in AdS3/CFT2, JHEP 05 (2018) 101 [arXiv:1804.02023] [INSPIRE].
A. Giveon, D. Kutasov and N. Seiberg, Comments on string theory on AdS(3), Adv. Theor. Math. Phys. 2 (1998) 733 [hep-th/9806194] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS(3) and SL(2,R) WZW model 1.: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [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].
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 et al., Superstrings on AdS3 at k = 1, JHEP 08 (2018) 204 [arXiv:1803.04420] [INSPIRE].
L. Eberhardt, A perturbative CFT dual for pure NS–NS AdS3 strings, J. Phys. A 55 (2022) 064001 [arXiv:2110.07535] [INSPIRE].
D. Berenstein and R.G. Leigh, Superstring perturbation theory and Ramond-Ramond backgrounds, Phys. Rev. D 60 (1999) 106002 [hep-th/9904104] [INSPIRE].
M. Cho, S. Collier and X. Yin, Strings in Ramond-Ramond Backgrounds from the Neveu-Schwarz-Ramond Formalism, JHEP 12 (2020) 123 [arXiv:1811.00032] [INSPIRE].
L. Eberhardt and K. Ferreira, The plane-wave spectrum from the worldsheet, JHEP 10 (2018) 109 [arXiv:1805.12155] [INSPIRE].
G. Arutyunov and S. Frolov, Foundations of the AdS5 × S5 Superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
A. Sfondrini, Towards integrability for AdS3/CFT2, J. Phys. A 48 (2015) 023001 [arXiv:1406.2971] [INSPIRE].
A. Cagnazzo and K. Zarembo, B-field in AdS(3)/CFT(2) Correspondence and Integrability, JHEP 11 (2012) 133 [Erratum ibid. 04 (2013) 003] [arXiv:1209.4049] [INSPIRE].
S. Frolov, D. Polvara and A. Sfondrini, On mixed-flux worldsheet scattering in AdS3/CFT2, JHEP 11 (2023) 055 [arXiv:2306.17553] [INSPIRE].
S. Frolov and A. Sfondrini, New dressing factors for AdS3/CFT2, JHEP 04 (2022) 162 [arXiv:2112.08896] [INSPIRE].
S. Frolov and A. Sfondrini, Mirror thermodynamic Bethe ansatz for AdS3/CFT2, JHEP 03 (2022) 138 [arXiv:2112.08898] [INSPIRE].
A. Cavaglià et al., Quantum Spectral Curve for AdS3/CFT2: a proposal, JHEP 12 (2021) 048 [arXiv:2109.05500] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 superYang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
A. Brollo, D. le Plat, A. Sfondrini and R. Suzuki, Tensionless Limit of Pure-Ramond-Ramond Strings and AdS3/CFT2, Phys. Rev. Lett. 131 (2023) 161604 [arXiv:2303.02120] [INSPIRE].
T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefański Jr., The complete worldsheet S matrix of superstrings on AdS3 × S3 × T4 with mixed three-form flux, Nucl. Phys. B 891 (2015) 570 [arXiv:1410.0866] [INSPIRE].
F.K. Seibold and A. Sfondrini, Transfer matrices for AdS3/CFT2, JHEP 05 (2022) 089 [arXiv:2202.11058] [INSPIRE].
S. Frolov, A. Pribytok and A. Sfondrini, Ground state energy of twisted AdS3 × S3 × T4 superstring and the TBA, JHEP 09 (2023) 027 [arXiv:2305.17128] [INSPIRE].
G. Arutyunov and S. Frolov, String hypothesis for the AdS5 × S5 mirror, JHEP 03 (2009) 152 [arXiv:0901.1417] [INSPIRE].
S. Frolov and A. Sfondrini, to appear.
A. Fontanella and A. Torrielli, Geometry of Massless Scattering in Integrable Superstring, JHEP 06 (2019) 116 [arXiv:1903.10759] [INSPIRE].
G. Arutyunov and S. Frolov, On String S-matrix, Bound States and TBA, JHEP 12 (2007) 024 [arXiv:0710.1568] [INSPIRE].
S. Frolov and A. Sfondrini, Massless S matrices for AdS3/CFT2, JHEP 04 (2022) 067 [arXiv:2112.08895] [INSPIRE].
P. Dorey and R. Tateo, Excited states by analytic continuation of TBA equations, Nucl. Phys. B 482 (1996) 639 [hep-th/9607167] [INSPIRE].
M. Baggio et al., Protected string spectrum in AdS3/CFT2 from worldsheet integrability, JHEP 04 (2017) 091 [arXiv:1701.03501] [INSPIRE].
S.J. van Tongeren, Introduction to the thermodynamic Bethe ansatz, J. Phys. A 49 (2016) 323005 [arXiv:1606.02951] [INSPIRE].
A.B. Zamolodchikov, On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories, Phys. Lett. B 253 (1991) 391 [INSPIRE].
L. Frappat, A. Sciarrino and P. Sorba, Structure of Basic Lie Superalgebras and of Their Affine Extensions, Commun. Math. Phys. 121 (1989) 457 [INSPIRE].
D. Chapovalov, M. Chapovalov, A. Lebedev and D. Leites, The classification of almost affine (hyperbolic) Lie superalgebras, J. Nonlin. Math. Phys. 17 (2010) 103 [arXiv:0906.1860] [INSPIRE].
A.B. Zamolodchikov, Thermodynamic Bethe Ansatz in Relativistic Models. Scaling Three State Potts and Lee-yang Models, Nucl. Phys. B 342 (1990) 695 [INSPIRE].
S. Frolov and R. Suzuki, Temperature quantization from the TBA equations, Phys. Lett. B 679 (2009) 60 [arXiv:0906.0499] [INSPIRE].
D. Tong, The holographic dual of AdS3 × S3 × S3 × S1, JHEP 04 (2014) 193 [arXiv:1402.5135] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański, The AdS3 × S3 × S3 × S1 worldsheet S matrix, J. Phys. A 48 (2015) 415401 [arXiv:1506.00218] [INSPIRE].
S. Ekhammar and D. Volin, Monodromy bootstrap for SU(2|2) quantum spectral curves: from Hubbard model to AdS3/CFT2, JHEP 03 (2022) 192 [arXiv:2109.06164] [INSPIRE].
A. Cavaglià, S. Ekhammar, N. Gromov and P. Ryan, Exploring the Quantum Spectral Curve for AdS3/CFT2, arXiv:2211.07810 [INSPIRE].
G. Arutyunov, S. Frolov and R. Suzuki, Exploring the mirror TBA, JHEP 05 (2010) 031 [arXiv:0911.2224] [INSPIRE].
G. Arutyunov and S. Frolov, The Dressing Factor and Crossing Equations, J. Phys. A 42 (2009) 425401 [arXiv:0904.4575] [INSPIRE].
N. Beisert, R. Hernandez and E. Lopez, A Crossing-symmetric phase for AdS5 × S5 strings, JHEP 11 (2006) 070 [hep-th/0609044] [INSPIRE].
S. Frolov, Konishi operator at intermediate coupling, J. Phys. A 44 (2011) 065401 [arXiv:1006.5032] [INSPIRE].
Acknowledgments
We thank Sergey Frolov, Alessandro Torrielli, Arkady Tseytlin, and Linus Wulff for useful related discussions. We are particularly grateful to Stefano Scopa for discussions and help with the Python code for the numerical solution of the TBA equations. DlP acknowledges support from the Stiftung der Deutschen Wirtschaft. The work of RS is supported by NSFC grant no. 12050410255. AS thanks the participants of the workshop “Integrability in Low-Supersymmetry Theories” in Filicudi, Italy, for a stimulating environment where part of this work was carried out. AS acknowledges support from the European Union — NextGenerationEU, and from the program STARS@UNIPD, under project “Exact-Holography — A new exact approach to holography: harnessing the power of string theory, conformal field theory, and integrable models.”
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: 2308.11576
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
Brollo, A., le Plat, D., Sfondrini, A. et al. More on the tensionless limit of pure-Ramond-Ramond AdS3/CFT2. J. High Energ. Phys. 2023, 160 (2023). https://doi.org/10.1007/JHEP12(2023)160
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2023)160