Abstract
We study superstring theory in three dimensional Anti-de Sitter spacetime with NS-NS flux, focusing on the case where the radius of curvature is equal to the string length. This corresponds to the critical level k = 1 in the formulation as a Wess-Zumino-Witten model. Previously, it was argued that a transition takes place at this special radius, from a phase dominated by black holes at larger radius to one dominated by long strings at smaller radius. We argue that the infinite tower of modes that become massless at k = 1 is a signal of this transition. We propose a simple two-dimensional conformal field theory as the holographic dual to superstring theory at k = 1. As evidence for our conjecture, we demonstrate that our putative dual exactly reproduces the full spectrum of the long strings of the weakly coupled string theory, including states unprotected by supersymmetry.
References
A. Giveon, D. Kutasov, E. Rabinovici and A. Sever, Phases of quantum gravity in AdS 3 and linear dilaton backgrounds, Nucl. Phys. B 719 (2005) 3 [hep-th/0503121] [INSPIRE].
M.R. Gaberdiel, R. Gopakumar and C. Hull, Stringy AdS 3 from the worldsheet, JHEP 07 (2017) 090 [arXiv:1704.08665] [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Superstring Collisions at Planckian Energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].
D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
B. Sundborg, Stringy gravity, interacting tensionless strings and massless higher spins, Nucl. Phys. Proc. Suppl. 102 (2001) 113 [hep-th/0103247] [INSPIRE].
E. Witten, Spacetime reconstruction, talk at the John Schwarz 60-th birthday symposium, November 2001, http://theory.caltech.edu/jhs60/witten/1.html.
A. Mikhailov, Notes on higher spin symmetries, hep-th/0201019 [INSPIRE].
U. Lindström and M. Zabzine, Tensionless strings, WZW models at critical level and massless higher spin fields, Phys. Lett. B 584 (2004) 178 [hep-th/0305098] [INSPIRE].
M. Kleban, A. Lawrence, M.M. Roberts and S. Storace, Metastability and instability in holographic gauge theories, JHEP 06 (2014) 152 [arXiv:1312.1312] [INSPIRE].
G.T. Horowitz and J. Polchinski, A correspondence principle for black holes and strings, Phys. Rev. D 55 (1997) 6189 [hep-th/9612146] [INSPIRE].
J.L.F. Barbon and E. Rabinovici, Touring the Hagedorn ridge, hep-th/0407236 [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].
K. Ferreira, M.R. Gaberdiel and J.I. Jottar, Higher spins on AdS 3 from the worldsheet, JHEP 07 (2017) 131 [arXiv:1704.08667] [INSPIRE].
G. Giribet, A. Pakman and L. Rastelli, Spectral Flow in AdS 3 /CFT 2, JHEP 06 (2008) 013 [arXiv:0712.3046] [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].
D. Israel, C. Kounnas and M.P. Petropoulos, Superstrings on NS5 backgrounds, deformed AdS 3 and holography, JHEP 10 (2003) 028 [hep-th/0306053] [INSPIRE].
S. Raju, Counting giant gravitons in AdS 3, Phys. Rev. D 77 (2008) 046012 [arXiv:0709.1171] [INSPIRE].
R. Argurio, A. Giveon and A. Shomer, Superstrings on AdS 3 and symmetric products, JHEP 12 (2000) 003 [hep-th/0009242] [INSPIRE].
A. Pakman, Unitarity of supersymmetric SL(2, ℝ)/U(1) and no ghost theorem for fermionic strings in AdS 3 × N, JHEP 01 (2003) 077 [hep-th/0301110] [INSPIRE].
B. Hoare and A.A. Tseytlin, Massive S-matrix of AdS 3 × S 3 × T 4 superstring theory with mixed 3-form flux, Nucl. Phys. B 873 (2013) 395 [arXiv:1304.4099] [INSPIRE].
T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefanski Jr., The complete worldsheet S matrix of superstrings on AdS 3 × S 3 × T 4 with mixed three-form flux, Nucl. Phys. B 891 (2015) 570 [arXiv:1410.0866] [INSPIRE].
M. Baggio, O. Ohlsson Sax, A. Sfondrini, B. Stefanski and A. Torrielli, Protected string spectrum in AdS 3 /CFT 2 from worldsheet integrability, JHEP 04 (2017) 091 [arXiv:1701.03501] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Stringy Symmetries and the Higher Spin Square, J. Phys. A 48 (2015) 185402 [arXiv:1501.07236] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, String Theory as a Higher Spin Theory, JHEP 09 (2016) 085 [arXiv:1512.07237] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
D. Kutasov and N. Seiberg, Noncritical superstrings, Phys. Lett. B 251 (1990) 67 [INSPIRE].
G.E. Giribet and D.E. Lopez-Fogliani, Remarks on free field realization of SL(2, ℝ)(k)/U(1) × U(1) WZNW model, JHEP 06 (2004) 026 [hep-th/0404231] [INSPIRE].
I. Runkel and G.M.T. Watts, A nonrational CFT with c = 1 as a limit of minimal models, JHEP 09 (2001) 006 [hep-th/0107118] [INSPIRE].
V. Schomerus, Rolling tachyons from Liouville theory, JHEP 11 (2003) 043 [hep-th/0306026] [INSPIRE].
D. Harlow, J. Maltz and E. Witten, Analytic Continuation of Liouville Theory, JHEP 12 (2011) 071 [arXiv:1108.4417] [INSPIRE].
R. Dijkgraaf, G.W. Moore, E.P. Verlinde and H.L. Verlinde, Elliptic genera of symmetric products and second quantized strings, Commun. Math. Phys. 185 (1997) 197 [hep-th/9608096] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, Four graviton scattering amplitude from S N R 8 supersymmetric orbifold σ-model, Nucl. Phys. B 524 (1998) 159 [hep-th/9712061] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and W. Li, A holographic dual for string theory on AdS 3 × S 3 × S 3 × S 1, JHEP 08 (2017) 111 [arXiv:1707.02705] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Tensionless string spectra on AdS 3, JHEP 05 (2018) 085 [arXiv:1803.04423] [INSPIRE].
O. Lunin and S.D. Mathur, Three point functions for M(N)/S(N) orbifolds with N = 4 supersymmetry, Commun. Math. Phys. 227 (2002) 385 [hep-th/0103169] [INSPIRE].
J.M. Maldacena, H. Ooguri and J. Son, Strings in AdS 3 and the SL(2, ℝ) WZW model. Part 2. Euclidean black hole, J. Math. Phys. 42 (2001) 2961 [hep-th/0005183] [INSPIRE].
M.R. Gaberdiel and I. Kirsch, Worldsheet correlators in AdS 3 /CFT 2, JHEP 04 (2007) 050 [hep-th/0703001] [INSPIRE].
A. Dabholkar and A. Pakman, Exact chiral ring of AdS 3 /CFT 2, Adv. Theor. Math. Phys. 13 (2009) 409 [hep-th/0703022] [INSPIRE].
J. de Boer, H. Ooguri, H. Robins and J. Tannenhauser, String theory on AdS 3, JHEP 12 (1998) 026 [hep-th/9812046] [INSPIRE].
G. Giribet and C.A. Núñez, Correlators in AdS 3 string theory, JHEP 06 (2001) 010 [hep-th/0105200] [INSPIRE].
C.A. Cardona and C.A. Núñez, Three-point functions in superstring theory on AdS 3 × S 3 × T 4, JHEP 06 (2009) 009 [arXiv:0903.2001] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS 3 and the SL(2, ℝ) WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006 [hep-th/0111180] [INSPIRE].
A. Pakman, L. Rastelli and S.S. Razamat, Diagrams for Symmetric Product Orbifolds, JHEP 10 (2009) 034 [arXiv:0905.3448] [INSPIRE].
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
ArXiv ePrint: 1803.04420
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Giribet, G., Hull, C., Kleban, M. et al. Superstrings on AdS3 at k = 1. J. High Energ. Phys. 2018, 204 (2018). https://doi.org/10.1007/JHEP08(2018)204
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)204
Keywords
- AdS-CFT Correspondence
- Long strings