Abstract
We present a systematic description of all warped AdS n × w M 10−n and \( {\mathbb{R}}^{n-1,1}{\times}_w{M}^{10-n} \) IIB backgrounds and identify the a priori number of supersymmetries N preserved by these solutions. In particular, we find that the AdS n backgrounds preserve \( N={2}^{\left[\frac{n}{2}\right]}k \) for n ≤ 4 and \( N={2}^{\left[\frac{n}{2}\right]+1}k \) for 4 < n ≤ 6 supersymmetries and for \( k\in {\mathbb{N}}_{+} \) suitably restricted. In addition under some assumptions required for the applicability of the maximum principle, we demonstrate that the Killing spinors of AdS n backgrounds can be identified with the zero modes of Dirac-like operators on M 10−n establishing a new class of Lichnerowicz type theorems. Furthermore, we adapt some of these results to \( {\mathbb{R}}^{n-1,1}{\times}_w{M}^{10-n} \) backgrounds with fluxes by taking the AdS radius to infinity. We find that these backgrounds preserve \( N={2}^{\left[\frac{n}{2}\right]}k \) for 2 < n ≤ 4 and \( N={2}^{\left[\frac{n+1}{2}\right]}k \) for 4 < n ≤ 7 supersymmetries. We also demonstrate that the Killing spinors of AdS n × w M 10−n do not factorize into Killing spinors on AdS n and Killing spinors on M 10−n.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P.G.O. Freund and M.A. Rubin, Dynamics of dimensional reduction, Phys. Lett. B 97 (1980) 233 [INSPIRE].
M.J. Duff, B.E.W. Nilsson and C.N. Pope, Kaluza-Klein supergravity, Phys. Rept. 130 (1986) 1 [INSPIRE].
M. Graña, Flux compactifications in string theory: a comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
L.J. Romans, New compactifications of chiral N = 2 D = 10 supergravity, Phys. Lett. B 153 (1985) 392 [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
B.S. Acharya, J.M. Figueroa-O’Farrill, C.M. Hull and B.J. Spence, Branes at conical singularities and holography, Adv. Theor. Math. Phys. 2 (1999) 1249 [hep-th/9808014] [INSPIRE].
M. Cvetič, H. Lü, C.N. Pope and J.F. Vazquez-Poritz, AdS in warped space-times, Phys. Rev. D 62 (2000) 122003 [hep-th/0005246] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of type IIB supergravity, Class. Quant. Grav. 23 (2006) 4693 [hep-th/0510125] [INSPIRE].
F. Apruzzi, M. Fazzi, A. Passias, D. Rosa and A. Tomasiello, AdS 6 solutions of type-II supergravity, JHEP 11 (2014) 099 [arXiv:1406.0852] [INSPIRE].
N.T. Macpherson, C. Núñez, L.A. Pando Zayas, V.G.J. Rodgers and C.A. Whiting, Type IIB supergravity solutions with AdS 5 from Abelian and non-Abelian T dualities, arXiv:1410.2650 [INSPIRE].
S. Beck, J. Gutowski and G. Papadopoulos, to appear.
J.M. Figueroa-O’Farrill and G. Papadopoulos, Maximally supersymmetric solutions of ten-dimensional and eleven-dimensional supergravities, JHEP 03 (2003) 048 [hep-th/0211089] [INSPIRE].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, N = 31 is not IIB, JHEP 02 (2007) 044 [hep-th/0606049] [INSPIRE].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, IIB solutions with N > 28 Killing spinors are maximally supersymmetric, JHEP 12 (2007) 070 [arXiv:0710.1829] [INSPIRE].
U. Gran, J. Gutowski and G. Papadopoulos, Classification of IIB backgrounds with 28 supersymmetries, JHEP 01 (2010) 044 [arXiv:0902.3642] [INSPIRE].
J. Figueroa-O’Farrill and N. Hustler, The homogeneity theorem for supergravity backgrounds, JHEP 10 (2012) 014 [arXiv:1208.0553] [INSPIRE].
U. Gran, J. Gutowski and G. Papadopoulos, AdS backgrounds from black hole horizons, Class. Quant. Grav. 30 (2013) 055014 [arXiv:1110.0479] [INSPIRE].
U. Gran, J. Gutowski and G. Papadopoulos, Index theory and dynamical symmetry enhancement near IIB horizons, JHEP 11 (2013) 104 [arXiv:1306.5765] [INSPIRE].
J. Grover, J.B. Gutowski, G. Papadopoulos and W.A. Sabra, Index theory and supersymmetry of 5D horizons, JHEP 06 (2014) 020 [arXiv:1303.0853] [INSPIRE].
J. Gutowski and G. Papadopoulos, Index theory and dynamical symmetry enhancement of M-horizons, JHEP 05 (2013) 088 [arXiv:1303.0869] [INSPIRE].
J.H. Schwarz and P.C. West, Symmetries and transformations of chiral N = 2 D = 10 supergravity, Phys. Lett. B 126 (1983) 301 [INSPIRE].
J.H. Schwarz, Covariant field equations of chiral N = 2 D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].
J.B. Gutowski and G. Papadopoulos, Supersymmetry of AdS and flat backgrounds in M-theory, arXiv:1407.5652 [INSPIRE].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, Systematics of IIB spinorial geometry, Class. Quant. Grav. 23 (2006) 1617 [hep-th/0507087] [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
F. Apruzzi, M. Fazzi, D. Rosa and A. Tomasiello, All AdS 7 solutions of type-II supergravity, JHEP 04 (2014) 064 [arXiv:1309.2949] [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: 1410.3431
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
Beck, S., Gutowski, J. & Papadopoulos, G. Supersymmetry of AdS and flat IIB backgrounds. J. High Energ. Phys. 2015, 20 (2015). https://doi.org/10.1007/JHEP02(2015)020
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2015)020