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Tensionless string spectra on AdS3

  • Matthias R. Gaberdiel
  • Rajesh Gopakumar
Open Access
Regular Article - Theoretical Physics

Abstract

The spectrum of superstrings on AdS3 × S3 × \( \mathbb{M} \)4 with pure NS-NS flux is analysed for the background where the radius of the AdS space takes the minimal value (k = 1). Both for \( \mathbb{M} \)4 = S3 × S1 and \( \mathbb{M} \)4 = \( \mathbb{T} \)4 we show that there is a special set of physical states, coming from the bottom of the spectrally flowed continuous representations, which agree in precise detail with the single particle spectrum of a free symmetric product orbifold. For the case of AdS3 × S3 × \( \mathbb{T} \)4 this relies on making sense of the world-sheet theory at k = 1, for which we make a concrete proposal. We also comment on the implications of this striking result.

Keywords

AdS-CFT Correspondence Conformal Field Theory 

Notes

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.

References

  1. [1]
    M.R. Gaberdiel and R. Gopakumar, Higher Spins & Strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    M.R. Gaberdiel and R. Gopakumar, Stringy Symmetries and the Higher Spin Square, J. Phys. A 48 (2015) 185402 [arXiv:1501.07236] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  3. [3]
    M.R. Gaberdiel and R. Gopakumar, String Theory as a Higher Spin Theory, JHEP 09 (2016) 085 [arXiv:1512.07237] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS d, Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [INSPIRE].
  5. [5]
    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].
  6. [6]
    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].
  7. [7]
    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].
  8. [8]
    M.R. Gaberdiel, R. Gopakumar and C. Hull, Stringy AdS 3 from the worldsheet, JHEP 07 (2017) 090 [arXiv:1704.08665] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    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].ADSCrossRefGoogle Scholar
  10. [10]
    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].
  11. [11]
    P. Goddard, D.I. Olive and G. Waterson, Superalgebras, Symplectic Bosons and the Sugawara Construction, Commun. Math. Phys. 112 (1987) 591 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    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].MathSciNetCrossRefGoogle Scholar
  13. [13]
    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].ADSCrossRefGoogle Scholar
  14. [14]
    S. Raju, Counting giant gravitons in AdS 3, Phys. Rev. D 77 (2008) 046012 [arXiv:0709.1171] [INSPIRE].
  15. [15]
    S. Elitzur, O. Feinerman, A. Giveon and D. Tsabar, String theory on AdS 3 × S 3 × S 3 × S 1, Phys. Lett. B 449 (1999) 180 [hep-th/9811245] [INSPIRE].
  16. [16]
    E.T. Whittaker and G.N. Watson, A Course of Modern Analysis, 4th edition, Cambridge University Press (1996).Google Scholar
  17. [17]
    S. Gukov, E. Martinec, G.W. Moore and A. Strominger, The Search for a holographic dual to AdS 3 × S 3 × S 3 × S 1, Adv. Theor. Math. Phys. 9 (2005) 435 [hep-th/0403090] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  18. [18]
    L. Eberhardt, M.R. Gaberdiel, R. Gopakumar and W. Li, BPS spectrum on AdS 3 × S 3 × S 3 × S 1, JHEP 03 (2017) 124 [arXiv:1701.03552] [INSPIRE].
  19. [19]
    D. Tong, The holographic dual of AdS 3 × S 3 × S 3 × S 1, JHEP 04 (2014) 193 [arXiv:1402.5135] [INSPIRE].
  20. [20]
    N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    C. Beem, W. Peelaers, L. Rastelli and B.C. van Rees, Chiral algebras of class S, JHEP 05 (2015) 020 [arXiv:1408.6522] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    R. Argurio, A. Giveon and A. Shomer, Superstrings on AdS 3 and symmetric products, JHEP 12 (2000) 003 [hep-th/0009242] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    J. Raeymaekers, On matter coupled to the higher spin square, J. Phys. A 49 (2016) 355402 [arXiv:1603.07845] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  24. [24]
    M. Sharma, The Higher Spin Rectangle, JHEP 01 (2018) 073 [arXiv:1708.04996] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    L. Rastelli and M. Wijnholt, Minimal AdS 3, Adv. Theor. Math. Phys. 11 (2007) 291 [hep-th/0507037] [INSPIRE].
  26. [26]
    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].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    V.G. Kac and M. Wakimoto, Modular invariant representations of infinite dimensional Lie algebras and superalgebras, Proc. Nat. Acad. Sci. 85 (1988) 4956 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    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].ADSCrossRefGoogle Scholar
  29. [29]
    R. Gopakumar, We need to talk (more) about AdS 3 /CF T 2, talk at Princeton Center for Theoretical Sciences, 2 November 2017 [http://pcts.princeton.edu/pcts/20YearsAdSCFT/slides+videos.html].
  30. [30]
    G. Giribet, C. Hull, M. Kleban, M. Porrati and E. Rabinovici, Superstrings on AdS 3 at k = 1, arXiv:1803.04420[INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Institut für Theoretische Physik, ETH ZurichZürichSwitzerland
  2. 2.International Centre for Theoretical Sciences-TIFRBengaluru NorthIndia

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