Abstract
In seven dimensions any spin manifold admits an SU(2) structure and therefore very general M-theory compactifications have the potential to allow for a reduction to N =4gaugedsupergravity. WeperformthisgeneralSU(2)reductionandgivetherelation of SU(2) torsion classes and fluxes to gaugings in the N = 4 theory. We furthermore show explicitly that this reduction is a consistent truncation of the eleven-dimensional theory, in other words classical solutions of the reduced theory also solve the eleven-dimensional equations of motion. This reduction generalizes previous M-theory reductions on TriSasakian manifolds and type IIA reductions on Calabi-Yau manifolds of vanishing Euler number. Moreover, it can also be applied to compactifications on certain G 2 holonomy manifolds and to more general flux backgrounds.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.-K. Kashani-Poor, R. Minasian and H. Triendl, Enhanced supersymmetry from vanishing Euler number, JHEP 04 (2013) 058 [arXiv:1301.5031] [INSPIRE].
R.A. Reid-Edwards and B. Spanjaard, N = 4 Gauged Supergravity from Duality-Twist Compactifications of String Theory, JHEP 12 (2008) 052 [arXiv:0810.4699] [INSPIRE].
H. Triendl and J. Louis, Type II compactifications on manifolds with SU(2) × SU(2) structure, JHEP 07 (2009) 080 [arXiv:0904.2993] [INSPIRE].
J. Louis, D. Martinez-Pedrera and A. Micu, Heterotic compactifications on SU(2)-structure backgrounds, JHEP 09 (2009) 012 [arXiv:0907.3799] [INSPIRE].
T. Danckaert, J. Louis, D. Martinez-Pedrera, B. Spanjaard and H. Triendl, The N = 4 effective action of type IIA supergravity compactified on SU(2)-structure manifolds, JHEP 08 (2011) 024 [arXiv:1104.5174] [INSPIRE].
T.W. Grimm, A. Kapfer and S. Lüst, Partial Supergravity Breaking and the Effective Action of Consistent Truncations, JHEP 02 (2015) 093 [arXiv:1409.0867] [INSPIRE].
B. de Wit, H. Samtleben and M. Trigiante, Magnetic charges in local field theory, JHEP 09 (2005) 016 [hep-th/0507289] [INSPIRE].
J. Schon and M. Weidner, Gauged N = 4 supergravities, JHEP 05 (2006) 034 [hep-th/0602024] [INSPIRE].
E. Thomas, Vector fields on manifolds, Bull. Amer. Math. Soc. 75 (1969) 643.
T. Friedrich, I. Kath, A. Moroianu and U. Semmelmann, On nearly parallel G 2 -structures, J. Geom. Phys. 23 (1997) 259 [hal-00126037].
P. Kaste, R. Minasian and A. Tomasiello, Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G structures, JHEP 07 (2003) 004 [hep-th/0303127] [INSPIRE].
D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [arXiv:1003.4283] [INSPIRE].
J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to N = 4 supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [INSPIRE].
D. Cassani and A.F. Faedo, A Supersymmetric consistent truncation for conifold solutions, Nucl. Phys. B 843 (2011) 455 [arXiv:1008.0883] [INSPIRE].
I. Bena, G. Giecold, M. Graña, N. Halmagyi and F. Orsi, Supersymmetric Consistent Truncations of IIB on T 1,1, JHEP 04 (2011) 021 [arXiv:1008.0983] [INSPIRE].
E. Ó Colgáin and O. Varela, Consistent reductions from D = 11 beyond Sasaki-Einstein, Phys. Lett. B 703 (2011) 180 [arXiv:1106.4781] [INSPIRE].
D. Cassani and P. Koerber, Tri-Sasakian consistent reduction, JHEP 01 (2012) 086 [arXiv:1110.5327] [INSPIRE].
D. Cassani, P. Koerber and O. Varela, All homogeneous N = 2 M-theory truncations with supersymmetric AdS 4 vacua, JHEP 11 (2012) 173 [arXiv:1208.1262] [INSPIRE].
D. Joyce, Compact Riemannian 7-manifolds with holonomy G 2 . I, J. Differ. Geom. 43 (1996) 291.
D. Joyce, Compact Riemannian 7-manifolds with holonomy G 2 . II, J. Differ. Geom. 43 (1996) 329.
G. Papadopoulos and P.K. Townsend, Compactification of D = 11 supergravity on spaces of exceptional holonomy, Phys. Lett. B 357 (1995) 300 [hep-th/9506150] [INSPIRE].
E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].
S. Kachru and A.-K. Kashani-Poor, Moduli potentials in type IIA compactifications with RR and NS flux, JHEP 03 (2005) 066 [hep-th/0411279] [INSPIRE].
J. Louis and H. Triendl, Maximally supersymmetric AdS 4 vacua in N = 4 supergravity, JHEP 10 (2014) 007 [arXiv:1406.3363] [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: 1505.05526
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
Triendl, H. Consistent truncations of M-theory for general SU(2) structures. J. High Energ. Phys. 2015, 68 (2015). https://doi.org/10.1007/JHEP09(2015)068
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2015)068