Abstract
We expand upon a claim made in a recent paper [arXiv:1411.5721] that generic minimally supersymmetric AdS backgrounds of warped flux compactifications of Type II and M theory can be understood as satisfying a straightforward weak integrability condition in the language of \( {E}_{d(d)}\times {\mathrm{\mathbb{R}}}^{+} \) generalised geometry. Namely, they are spaces admitting a generalised G-structure set by the Killing spinor and with constant singlet generalised intrinsic torsion.
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.P. Gauntlett, D. Martelli, S. Pakis and D. Waldram, G structures and wrapped NS5-branes, Commun. Math. Phys. 247 (2004) 421 [hep-th/0205050] [INSPIRE].
J.P. Gauntlett and S. Pakis, The Geometry of D = 11 Killing spinors, JHEP 04 (2003) 039 [hep-th/0212008] [INSPIRE].
D. Martelli and J. Sparks, G structures, fluxes and calibrations in M-theory, Phys. Rev. D 68 (2003) 085014 [hep-th/0306225] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of M-theory, Class. Quant. Grav. 21 (2004) 4335 [hep-th/0402153] [INSPIRE].
A. Lukas and P.M. Saffin, M theory compactification, fluxes and AdS 4, Phys. Rev. D 71 (2005) 046005 [hep-th/0403235] [INSPIRE].
K. Behrndt and C. Jeschek, Fluxes in M-theory on 7-manifolds: G 2− , SU(3) and SU(2)-structures, hep-th/0406138 [INSPIRE].
D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [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].
M. Gabella, D. Martelli, A. Passias and J. Sparks, \( \mathcal{N}=2 \) supersymmetric AdS 4 solutions of M-theory, Commun. Math. Phys. 325 (2014) 487 [arXiv:1207.3082] [INSPIRE].
R. Minasian, M. Petrini and A. Zaffaroni, Gravity duals to deformed SYM theories and Generalized Complex Geometry, JHEP 12 (2006) 055 [hep-th/0606257] [INSPIRE].
M. Gabella, J.P. Gauntlett, E. Palti, J. Sparks and D. Waldram, AdS 5 Solutions of Type IIB Supergravity and Generalized Complex Geometry, Commun. Math. Phys. 299 (2010) 365 [arXiv:0906.4109] [INSPIRE].
M. Gabella and J. Sparks, Generalized Geometry in AdS/CFT and Volume Minimization, Nucl. Phys. B 861 (2012) 53 [arXiv:1011.4296] [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].
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, A. Passias and A. Tomasiello, Supersymmetric AdS 5 solutions of massive IIA supergravity, JHEP 06 (2015) 195 [arXiv:1502.06620] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supersymmetric Backgrounds and Generalised Special Holonomy, Class. Quant. Grav. 33 (2016) 125026 [arXiv:1411.5721] [INSPIRE].
C.M. Hull, Generalised Geometry for M-theory, JHEP 07 (2007) 079 [hep-th/0701203] [INSPIRE].
P. Pires Pacheco and D. Waldram, M-theory, exceptional generalised geometry and superpotentials, JHEP 09 (2008) 123 [arXiv:0804.1362] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, \( {E}_{d(d)}\times {\mathrm{\mathbb{R}}}^{+} \) generalised geometry, connections and M-theory, JHEP 02 (2014) 054 [arXiv:1112.3989] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry II: \( {E}_{d(d)}\times {\mathrm{\mathbb{R}}}^{+} \) and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
M. Graña and F. Orsi, N = 1 vacua in Exceptional Generalized Geometry, JHEP 08 (2011) 109 [arXiv:1105.4855] [INSPIRE].
M. Graña and F. Orsi, N = 2 vacua in Generalized Geometry, JHEP 11 (2012) 052 [arXiv:1207.3004] [INSPIRE].
W. Nahm, Supersymmetries and their Representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
A. Coimbra and C. Strickland-Constable, Supersymmetric Backgrounds, the Killing Superalgebra and Generalised Special Holonomy, arXiv:1606.09304 [INSPIRE].
P.G.O. Freund and M.A. Rubin, Dynamics of Dimensional Reduction, Phys. Lett. B 97 (1980) 233 [INSPIRE].
A. Bilal, J.-P. Derendinger and K. Sfetsos, (Weak) G 2 holonomy from selfduality, flux and supersymmetry, Nucl. Phys. B 628 (2002) 112 [hep-th/0111274] [INSPIRE].
A. Gray, Weak holonomy groups, Math. Z. 123 (1971) 290.
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].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, arXiv:1401.3360 [INSPIRE].
E.M. Babalic and C.I. Lazaroiu, Foliated eight-manifolds for M-theory compactification, JHEP 01 (2015) 140 [arXiv:1411.3148] [INSPIRE].
E.M. Babalic and C.I. Lazaroiu, Singular foliations for M-theory compactification, JHEP 03 (2015) 116 [arXiv:1411.3497] [INSPIRE].
M. Graña, C.S. Shahbazi and M. Zambon, Spin(7)-manifolds in compactifications to four dimensions, JHEP 11 (2014) 046 [arXiv:1405.3698] [INSPIRE].
C. Strickland-Constable, Subsectors, Dynkin Diagrams and New Generalised Geometries, arXiv:1310.4196 [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: 1504.02465
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
Coimbra, A., Strickland-Constable, C. Generalised structures for \( \mathcal{N}=1 \) AdS backgrounds. J. High Energ. Phys. 2016, 92 (2016). https://doi.org/10.1007/JHEP11(2016)092
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2016)092