Abstract
We propose a class of AdS3/CFT2 dualities with \( \mathcal{N} \) = (2, 2) supersymmetry. These dualities relate string theory on \( {\mathrm{AdS}}_3\times \left({\mathrm{S}}^3\times {\mathbb{T}}^4\right)/\mathrm{G} \) to marginal deformations of the symmetric product orbifold of \( {\mathbb{T}}^4/\mathrm{G} \), where G is a dihedral group. We demonstrate that the BPS spectrum calculated from supergravity and string theory agrees with that of the dual CFT. Moreover, the supergravity elliptic genus is shown to reproduce the CFT answer, thus providing further non-trivial evidence in favour of the proposal.
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, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept. 369 (2002) 549 [hep-th/0203048] [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].
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].
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].
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].
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].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 dual for minimal model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [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. Ronne, Higher spin AdS 3 supergravity and its dual CFT, JHEP 02 (2012) 109 [arXiv:1111.2139] [INSPIRE].
C. Candu and M.R. Gaberdiel, Supersymmetric holography on AdS 3, JHEP 09 (2013) 071 [arXiv:1203.1939] [INSPIRE].
C.-M. Chang, S. Minwalla, T. Sharma and X. Yin, ABJ triality: from higher spin fields to strings, J. Phys. A 46 (2013) 214009 [arXiv:1207.4485] [INSPIRE].
C. Vafa, Modular invariance and discrete torsion on orbifolds, Nucl. Phys. B 273 (1986) 592 [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
T. Banks and L.J. Dixon, Constraints on string vacua with space-time supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].
L. Eberhardt, Supersymmetric AdS 3 supergravity backgrounds and holography, arXiv:1710.09826 [INSPIRE].
L.C. Grove and C.T. Benson, Finite reflection groups, Springer Science & Business Media 99, (1996).
D. Handel, On products in the cohomology of the dihedral groups, Tohoku Math. J. 45 (1993) 13.
M.R. Gaberdiel, Discrete torsion orbifolds and D-branes, JHEP 11 (2000) 026 [hep-th/0008230] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal field theory, Springer, New York U.S.A., (1997) [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].
T. Kawai, Y. Yamada and S.-K. Yang, Elliptic genera and N = 2 superconformal field theory, Nucl. Phys. B 414 (1994) 191 [hep-th/9306096] [INSPIRE].
M. Eichler and D. Zagier, The theory of Jacobi forms, Birkhäuser, (1985).
I.S. Gradshteyn and I.M. Ryzhik, Table of integrals, series, and products, 6th ed., Academic Press, U.S.A., (2000).
J. de Boer, Large-N elliptic genus and AdS/CFT correspondence, JHEP 05 (1999) 017 [hep-th/9812240] [INSPIRE].
C. Bär, Real Killing spinors and holonomy, Commun. Math. Phys. 154 (1993) 509.
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański, The complete AdS 3×S 3×T 4 worldsheet S matrix, JHEP 10 (2014) 066 [arXiv:1406.0453] [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].
J. de Boer, Six-dimensional supergravity on S 3×AdS 3 and 2D conformal field theory, Nucl. Phys. B 548 (1999) 139 [hep-th/9806104] [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].
M.R. Gaberdiel, T. Hartman and K. Jin, Higher spin black holes from CFT, JHEP 04 (2012) 103 [arXiv:1203.0015] [INSPIRE].
N. Seiberg and E. Witten, The D1/D5 system and singular CFT, JHEP 04 (1999) 017 [hep-th/9903224] [INSPIRE].
T. Banks, L.J. Dixon, D. Friedan and E.J. Martinec, Phenomenology and conformal field theory or can string theory predict the weak mixing angle?, Nucl. Phys. B 299 (1988) 613 [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Large-N = 4 holography, JHEP 09 (2013) 036 [arXiv:1305.4181] [INSPIRE].
E. Gava, A.B. Hammou, J.F. Morales and K.S. Narain, AdS/CFT correspondence and D1/D5 systems in theories with 16 supercharges, JHEP 03 (2001) 035 [hep-th/0102043] [INSPIRE].
S. Hohenegger, C.A. Keller and I. Kirsch, Heterotic AdS 3 /CFT 2 duality with (0, 4) spacetime supersymmetry, Nucl. Phys. B 804 (2008) 193 [arXiv:0804.4066] [INSPIRE].
T. Hartman, C.A. Keller and B. Stoica, Universal spectrum of 2d conformal field theory in the large c limit, JHEP 09 (2014) 118 [arXiv:1405.5137] [INSPIRE].
F.M. Haehl and M. Rangamani, Permutation orbifolds and holography, JHEP 03 (2015) 163 [arXiv:1412.2759] [INSPIRE].
A. Belin, C.A. Keller and A. Maloney, String universality for permutation orbifolds, Phys. Rev. D 91 (2015) 106005 [arXiv:1412.7159] [INSPIRE].
A. Belin, C.A. Keller and A. Maloney, Permutation orbifolds in the large-N limit, Annales Henri Poincaré (2016) 1 [arXiv:1509.01256] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Ronne, Extended higher spin holography and Grassmannian models, JHEP 11 (2013) 038 [arXiv:1306.0466] [INSPIRE].
C. Candu, C. Peng and C. Vollenweider, Extended supersymmetry in AdS 3 higher spin theories, JHEP 12 (2014) 113 [arXiv:1408.5144] [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: 1709.06393
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Datta, S., Eberhardt, L. & Gaberdiel, M.R. Stringy \( \mathcal{N} \) = (2, 2) holography for AdS3. J. High Energ. Phys. 2018, 146 (2018). https://doi.org/10.1007/JHEP01(2018)146
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2018)146