Abstract
We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that AdS n × w M 10 − n preserve \( {2}^{\left[\frac{n}{2}\right]}k \) for n ≤ 4 and \( {2}^{\left[\frac{n}{2}\right]+1}k \) for 4 < n ≤ 7 supersymmetries, k ∈ ℕ >0. In addition we show that, for suitably restricted fields and M 10 − n, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on M 10 − n. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to ℝ 1,n − 1 × w M 10 − n backgrounds which underpin flux compactifications to ℝ 1,n − 1 and show that these preserve \( {2}^{\left[\frac{n}{2}\right]}k \) for \( 2<n\le\ 4,\ {2}^{\left[\frac{n+1}{2}\right]}k \) for 4 < n ≤ 8, and \( {2}^{\left[\frac{n}{2}\right]}k \) for n = 9, 10 supersymmetries.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
P.G.O. Freund and M.A. Rubin, Dynamics of dimensional reduction, Phys. Lett. B 97 (1980) 233 [INSPIRE].
L.J. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett. B 169 (1986) 374 [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].
D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [INSPIRE].
D. Lüst and D. Tsimpis, New supersymmetric AdS 4 type-II vacua, JHEP 09 (2009) 098 [arXiv:0906.2561] [INSPIRE].
F. Apruzzi, M. Fazzi, A. Passias, D. Rosa and A. Tomasiello, AdS 6 solutions of type-II supergravity, JHEP 11 (2014) 099 [Erratum ibid. 05 (2015) 012] [arXiv:1406.0852] [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].
J.B. Gutowski and G. Papadopoulos, Supersymmetry of AdS and flat backgrounds in M-theory, JHEP 02 (2015) 145 [arXiv:1407.5652] [INSPIRE].
S.W. Beck, J.B. Gutowski and G. Papadopoulos, Supersymmetry of AdS and flat IIB backgrounds, JHEP 02 (2015) 020 [arXiv:1410.3431] [INSPIRE].
M. Huq and M.A. Namazie, Kaluza-Klein supergravity in ten-dimensions, Class. Quant. Grav. 2 (1985) 293 [Erratum ibid. 2 (1985) 597] [INSPIRE].
F. Giani and M. Pernici, N = 2 supergravity in ten-dimensions, Phys. Rev. D 30 (1984) 325 [INSPIRE].
I.C.G. Campbell and P.C. West, N = 2 D = 10 nonchiral supergravity and its spontaneous compactification, Nucl. Phys. B 243 (1984) 112 [INSPIRE].
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, U. Kayani and G. Papadopoulos, Dynamical symmetry enhancement near IIA horizons, JHEP 06 (2015) 139 [arXiv:1409.6303] [INSPIRE].
U. Gran, J. Gutowski, U. Kayani and G. Papadopoulos, Dynamical symmetry enhancement near massive IIA horizons, arXiv:1411.5286 [INSPIRE].
J. Figueroa-O’Farrill and N. Hustler, The homogeneity theorem for supergravity backgrounds, JHEP 10 (2012) 014 [arXiv:1208.0553] [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].
U. Gran, J. Gutowski and G. Papadopoulos, AdS backgrounds from black hole horizons, Class. Quant. Grav. 30 (2013) 055014 [arXiv:1110.0479] [INSPIRE].
I.A. Bandos, J.A. de Azcarraga and O. Varela, On the absence of BPS preonic solutions in IIA and IIB supergravities, JHEP 09 (2006) 009 [hep-th/0607060] [INSPIRE].
E.A. Bergshoeff, J. Hartong, P.S. Howe, T. Ortín and F. Riccioni, IIA/IIB supergravity and ten-forms, JHEP 05 (2010) 061 [arXiv:1004.1348] [INSPIRE].
U. Gran, G. Papadopoulos and C. von Schultz, Supersymmetric geometries of IIA supergravity I, JHEP 05 (2014) 024 [arXiv:1401.6900] [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: 1501.07620
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 IIA warped flux AdS and flat backgrounds. J. High Energ. Phys. 2015, 135 (2015). https://doi.org/10.1007/JHEP09(2015)135
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2015)135