Abstract
The BPS spectrum of string theory on AdS3 × S3 × S3 × S1 is determined using a world-sheet description in terms of WZW models. It is found that the theory only has BPS states with j + = j − where j ± refer to the spins of the \( \mathfrak{s}\mathfrak{u}(2) \) algebras of the large \( \mathcal{N} \) = 4 superconformal algebra. We then re-examine the BPS spectrum of the corresponding supergravity and find that, contrary to previous claims in the literature, also in supergravity only the states with j + = j − are BPS. This resolves a number of long-standing puzzles regarding the BPS spectrum of string theory and supergravity in this background.
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References
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].
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, J. Manschot, K. Papadodimas and E. Verlinde, The chiral ring of AdS 3 /CFT 2 and the attractor mechanism, JHEP 03 (2009) 030 [arXiv:0809.0507] [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Higher Spins & Strings, JHEP 11 (2014) 044 [arXiv:1406.6103] [INSPIRE].
M. Ademollo et al., Dual String Models with Nonabelian Color and Flavor Symmetries, Nucl. Phys. B 114 (1976) 297 [INSPIRE].
T. Eguchi and A. Taormina, Unitary Representations of N = 4 Superconformal Algebra, Phys. Lett. B 196 (1987) 75 [INSPIRE].
T. Eguchi and A. Taormina, Character Formulas for the N = 4 Superconformal Algebra, Phys. Lett. B 200 (1988) 315 [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].
A. Sevrin, W. Troost and A. Van Proeyen, Superconformal Algebras in Two-Dimensions with N = 4, Phys. Lett. B 208 (1988) 447 [INSPIRE].
K. Schoutens, O(n) Extended Superconformal Field Theory in Superspace, Nucl. Phys. B 295 (1988) 634 [INSPIRE].
P. Spindel, A. Sevrin, W. Troost and A. Van Proeyen, Extended Supersymmetric σ-models on Group Manifolds. 1. The Complex Structures, Nucl. Phys. B 308 (1988) 662 [INSPIRE].
A. Van Proeyen, Realizations of N = 4 Superconformal Algebras on Wolf Spaces, Class. Quant. Grav. 6 (1989) 1501 [INSPIRE].
A. Sevrin and G. Theodoridis, N = 4 superconformal coset theories, Nucl. Phys. B 332 (1990) 380 [INSPIRE].
M. Günaydin, J.L. Petersen, A. Taormina and A. Van Proeyen, On the Unitary Representations of a Class of N = 4 Superconformal Algebras, Nucl. Phys. B 322 (1989) 402 [INSPIRE].
J.L. Petersen and A. Taormina, Characters of the N = 4 Superconformal Algebra With Two Central Extensions, Nucl. Phys. B 331 (1990) 556 [INSPIRE].
J.L. Petersen and A. Taormina, Characters of the N = 4 Superconformal Algebra With Two Central Extensions: 2. Massless Representations, Nucl. Phys. B 333 (1990) 833 [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. 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.M. Maldacena and H. Ooguri, Strings in AdS 3 and \( \mathrm{S}\mathrm{L}\left(2,\mathbb{R}\right) \) WZW model 1.: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
S. Deger, A. Kaya, E. Sezgin and P. Sundell, Spectrum of D = 6, N = 4b supergravity on AdS in three-dimensions ×S 3, Nucl. Phys. B 536 (1998) 110 [hep-th/9804166] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel, R. Gopakumar and W. Li, in progress.
P. Di Vecchia, V.G. Knizhnik, J.L. Petersen and P. Rossi, A Supersymmetric Wess-Zumino Lagrangian in Two-Dimensions, Nucl. Phys. B 253 (1985) 701 [INSPIRE].
J.M. Evans, M.R. Gaberdiel and M.J. Perry, The no ghost theorem for AdS 3 and the stringy exclusion principle, Nucl. Phys. B 535 (1998) 152 [hep-th/9806024] [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].
T. Ortin, Gravity and strings, Cambridge University Press (2004).
M. Baggio, O. Ohlson Sax, A. Sfondrini, B. Stefanski and A. Torielli, Protected string spectrum in AdS 3 /CFT 2 from worldsheet integrability, to appear.
S. Gukov, E. Martinec, G.W. Moore and A. Strominger, An index for 2-D field theories with large N = 4 superconformal symmetry, hep-th/0404023 [INSPIRE].
M.R. Gaberdiel and R. Gopakumar, Large-N =4 Holography, JHEP 09 (2013) 036 [arXiv:1305.4181] [INSPIRE].
M. Günaydin, G. Sierra and P.K. Townsend, The Unitary Supermultiplets of d = 3 Anti-de Sitter and d = 2 Conformal Superalgebras, Nucl. Phys. B 274 (1986) 429 [INSPIRE].
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Eberhardt, L., Gaberdiel, M.R., Gopakumar, R. et al. BPS spectrum on AdS3×S3×S3×S1 . J. High Energ. Phys. 2017, 124 (2017). https://doi.org/10.1007/JHEP03(2017)124
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DOI: https://doi.org/10.1007/JHEP03(2017)124