Abstract
A new family of higher spin algebras that arises upon restricting matrix extensions of \( \mathfrak{s}\mathfrak{h}\mathfrak{s}\left[\lambda \right] \) is found. We identify coset CFTs realising these symmetry algebras, and thus propose new higher spin-CFT dual pairs. These higher spin theories arise naturally as a subsector of string theory on AdS3 × S3 × S3 × S1 for specific ratios of the radii of the two spheres.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.F. Prokushkin and M.A. Vasiliev, Higher spin gauge interactions for massive matter fields in 3-D AdS space-time, Nucl. Phys. B 545 (1999) 385 [hep-th/9806236] [INSPIRE].
S. Prokushkin and M.A. Vasiliev, 3-D higher spin gauge theories with matter, in Theory of elementary particles. Proceedings, 31st International Symposium Ahrenshoop, Buckow, Germany, September 2-6, 1997, 1998, hep-th/9812242 [INSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W ∞ as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [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, Minimal Model Holography, J. Phys. A 46 (2013) 214002 [arXiv:1207.6697] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, hep-th/9910096 [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Higher Spins & Strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [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].
E. Bergshoeff, M.A. Vasiliev and B. de Wit, The super-W ∞(λ) algebra, Phys. Lett. B 256 (1991) 199 [INSPIRE].
E. Bergshoeff, B. de Wit and M.A. Vasiliev, The structure of the super-W ∞(λ) algebra, Nucl. Phys. B 366 (1991) 315 [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Large N = 4 Holography, JHEP 09 (2013) 036 [arXiv:1305.4181] [INSPIRE].
T. Creutzig, Y. Hikida and P.B. Ronne, Extended higher spin holography and Grassmannian models, JHEP 11 (2013) 038 [arXiv:1306.0466] [INSPIRE].
M.A. Vasiliev, Extended Higher Spin Superalgebras and Their Realizations in Terms of Quantum Operators, Fortsch. Phys. 36 (1988) 33 [INSPIRE].
M. Henneaux, G. Lucena Gómez, J. Park and S.-J. Rey, Super-W ∞ Asymptotic Symmetry of Higher-Spin AdS 3 Supergravity, JHEP 06 (2012) 037 [arXiv:1203.5152] [INSPIRE].
C. Candu, C. Peng and C. Vollenweider, Extended supersymmetry in AdS 3 higher spin theories, JHEP 12 (2014) 113 [arXiv:1408.5144] [INSPIRE].
M.R. Gaberdiel and T. Hartman, Symmetries of Holographic Minimal Models, JHEP 05 (2011) 031 [arXiv:1101.2910] [INSPIRE].
A. Campoleoni, S. Fredenhagen and S. Pfenninger, Asymptotic W-symmetries in three-dimensional higher-spin gauge theories, JHEP 09 (2011) 113 [arXiv:1107.0290] [INSPIRE].
C. Candu and M.R. Gaberdiel, Duality in \( \mathcal{N} \) = 2 Minimal Model Holography, JHEP 02 (2013) 070 [arXiv:1207.6646] [INSPIRE].
M. Beccaria, C. Candu and M.R. Gaberdiel, The large \( \mathcal{N} \) = 4 superconformal W ∞ algebra, JHEP 06 (2014) 117 [arXiv:1404.1694] [INSPIRE].
C. Candu and M.R. Gaberdiel, Supersymmetric holography on AdS 3, JHEP 09 (2013) 071 [arXiv:1203.1939] [INSPIRE].
C. Candu, M.R. Gaberdiel, M. Kelm and C. Vollenweider, Even spin minimal model holography, JHEP 01 (2013) 185 [arXiv:1211.3113] [INSPIRE].
M.R. Gaberdiel and M. Kelm, The continuous orbifold of \( \mathcal{N} \) = 2 minimal model holography, JHEP 08 (2014) 084 [arXiv:1406.2345] [INSPIRE].
K. Ferreira and M.R. Gaberdiel, The \( \mathfrak{so} \) -Kazama-Suzuki Models at Large Level, JHEP 04 (2015) 017 [arXiv:1412.7213] [INSPIRE].
K. Ferreira, Even spin \( \mathcal{N} \) = 4 holography, JHEP 09 (2017) 110 [arXiv:1702.02641] [INSPIRE].
M.R. Gaberdiel and P. Suchanek, Limits of Minimal Models and Continuous Orbifolds, JHEP 03 (2012) 104 [arXiv:1112.1708] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Springer (1997).
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].
P. Bouwknegt and K. Schoutens, \( \mathcal{W} \) symmetry in conformal field theory, Phys. Rept. 223 (1993) 183 [hep-th/9210010] [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].
J. de Boer, A. Pasquinucci and K. Skenderis, AdS/CFT dualities involving large 2-D N = 4 superconformal symmetry, Adv. Theor. Math. Phys. 3 (1999) 577 [hep-th/9904073] [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].
D. Tong, The holographic dual of AdS 3 × S 3 × S 3 × S 1, JHEP 04 (2014) 193 [arXiv:1402.5135] [INSPIRE].
M. Baggio, O. Ohlsson Sax, A. Sfondrini, B. Stefanski and A. Torrielli, Protected string spectrum in AdS 3 /CF T 2 from worldsheet integrability, JHEP 04 (2017) 091 [arXiv:1701.03501] [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].
A. Sevrin, W. Troost and A. Van Proeyen, Superconformal Algebras in Two-Dimensions with N = 4, Phys. Lett. B 208 (1988) 447 [INSPIRE].
S. Datta, L. Eberhardt and M.R. Gaberdiel, Stringy \( \mathcal{N} \) = (2, 2) holography for AdS 3, JHEP 01 (2018) 146 [arXiv:1709.06393] [INSPIRE].
M. Baggio, M.R. Gaberdiel and C. Peng, Higher spins in the symmetric orbifold of K3, Phys. Rev. D 92 (2015) 026007 [arXiv:1504.00926] [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].
E. Bergshoeff, C.N. Pope, L.J. Romans, E. Sezgin and X. Shen, The Super W ∞ Algebra, Phys. Lett. B 245 (1990) 447 [INSPIRE].
R. Blumenhagen, M. Flohr, A. Kliem, W. Nahm, A. Recknagel and R. Varnhagen, W algebras with two and three generators, Nucl. Phys. B 361 (1991) 255 [INSPIRE].
K. Thielemans, A Mathematica package for computing operator product expansions, Int. J. Mod. Phys. C 2 (1991) 787 [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: 1801.00806
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
Eberhardt, L., Gaberdiel, M.R. & Rienäcker, I. Higher spin algebras and large \( \mathcal{N} \) = 4 holography. J. High Energ. Phys. 2018, 97 (2018). https://doi.org/10.1007/JHEP03(2018)097
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2018)097