Abstract
We consider a class of (orbifolds of) M-theory compactifications on Sd × T 7−d with gauge fluxes yielding minimally supersymmetric STU-models in 4D. We present a group-theoretical derivation of the corresponding flux-induced superpotentials and argue that the aforementioned backgrounds provide a (globally) geometric origin for 4D theories that only look locally geometric from the perspective of twisted tori. In particular, we show that Q-flux can be used to generate compactifications on S4 × T 3. We thus conclude that the effect of turning on non-geometric fluxes, at least when the section condition is solved, may be recovered by considering reductions on different topologies other than toroidal.
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M.P. Hertzberg, S. Kachru, W. Taylor and M. Tegmark, Inflationary Constraints on Type IIA String Theory, JHEP 12 (2007) 095 [arXiv:0711.2512] [INSPIRE].
C. Caviezel, P. Koerber, S. Körs, D. Lüst, T. Wrase et al., On the Cosmology of Type IIA Compactifications on SU(3)-structure Manifolds, JHEP 04 (2009) 010 [arXiv:0812.3551] [INSPIRE].
U.H. Danielsson, S.S. Haque, P. Koerber, G. Shiu, T. Van Riet et al., de Sitter hunting in a classical landscape, Fortsch. Phys. 59 (2011) 897 [arXiv:1103.4858] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Charting the landscape of N = 4 flux compactifications, JHEP 03 (2011) 137 [arXiv:1102.0239] [INSPIRE].
G. Dall’Agata and N. Prezas, Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes, JHEP 10 (2005) 103 [hep-th/0509052] [INSPIRE].
J.-P. Derendinger and A. Guarino, A second look at gauged supergravities from fluxes in M-theory, JHEP 09 (2014) 162 [arXiv:1406.6930] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].
W.H. Baron and G. Dall’Agata, Uplifting non-compact gauged supergravities, JHEP 02 (2015) 003 [arXiv:1410.8823] [INSPIRE].
D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The Local symmetries of M-theory and their formulation in generalised geometry, JHEP 01 (2012) 012 [arXiv:1110.3930] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, \( {E_d}_{(d)}\times {\mathbb{R}}^{+} \) 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: \( {E_d}_{(d)}\times {\mathbb{R}}^{+} \) and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional Field Theory I: E 6(6) covariant Form of M-theory and Type IIB, Phys. Rev. D 89 (2014) 066016 [arXiv:1312.0614] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
O. Hohm and H. Samtleben, Consistent Kaluza-Klein Truncations via Exceptional Field Theory, JHEP 01 (2015) 131 [arXiv:1410.8145] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].
G. Dibitetto, J.J. Fernandez-Melgarejo, D. Marques and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys. 60 (2012) 1123 [arXiv:1203.6562] [INSPIRE].
E. Musaev and H. Samtleben, Fermions and supersymmetry in E 6(6) exceptional field theory, JHEP 03 (2015) 027 [arXiv:1412.7286] [INSPIRE].
B. de Carlos, A. Guarino and J.M. Moreno, Complete classification of Minkowski vacua in generalised flux models, JHEP 02 (2010) 076 [arXiv:0911.2876] [INSPIRE].
U. Danielsson and G. Dibitetto, On the distribution of stable de Sitter vacua, JHEP 03 (2013) 018 [arXiv:1212.4984] [INSPIRE].
J. Blabäck, U. Danielsson and G. Dibitetto, Fully stable dS vacua from generalised fluxes, JHEP 08 (2013) 054 [arXiv:1301.7073] [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].
B. de Wit, H. Samtleben and M. Trigiante, The Maximal D = 4 supergravities, JHEP 06 (2007)049 [arXiv:0705.2101] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, How to halve maximal supergravity, JHEP 06 (2011) 030 [arXiv:1104.3587] [INSPIRE].
G. Aldazabal, P.G. Camara and J.A. Rosabal, Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications, Nucl. Phys. B 814 (2009) 21 [arXiv:0811.2900] [INSPIRE].
G. Dall’Agata, G. Villadoro and F. Zwirner, Type- IIA flux compactifications and N = 4 gauged supergravities, JHEP 08 (2009) 018 [arXiv:0906.0370] [INSPIRE].
G. Aldazabal, P.G. Camara, A. Font and L.E. Ibáñez, More dual fluxes and moduli fixing, JHEP 05 (2006) 070 [hep-th/0602089] [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Lobotomy of Flux Compactifications, JHEP 05 (2014)067 [arXiv:1402.4478] [INSPIRE].
U.H. Danielsson, G. Shiu, T. Van Riet and T. Wrase, A note on obstinate tachyons in classical dS solutions, JHEP 03 (2013) 138 [arXiv:1212.5178] [INSPIRE].
J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].
G. Dibitetto, A. Guarino and D. Roest, Exceptional Flux Compactifications, JHEP 05 (2012) 056 [arXiv:1202.0770] [INSPIRE].
B. de Wit and H. Nicolai, The Consistency of the S 7 Truncation in D = 11 Supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].
P.G.O. Freund and M.A. Rubin, Dynamics of Dimensional Reduction, Phys. Lett. B 97 (1980)233 [INSPIRE].
M.J. Duff, Supergravity, the Seven Sphere and Spontaneous Symmetry Breaking, Nucl. Phys. B 219 (1983) 389 [INSPIRE].
M. Duff and D. Toms, Kaluza-Klein-Kounterterms, CERN-TH-3259.
F. Englert, Spontaneous Compactification of Eleven-Dimensional Supergravity, Phys. Lett. B 119 (1982) 339 [INSPIRE].
M.J. Duff, Ultraviolet divergences in extended supergravity, arXiv:1201.0386 [INSPIRE].
M. Duff and C. Pope, Kaluza-klein Supergravity And The Seven Sphere, in proceeding Supersymmetry and Supergravity, Trieste, 1982, ICTP-82-83-7.
G. Dall’Agata and G. Inverso, On the Vacua of N = 8 Gauged Supergravity in 4 Dimensions, Nucl. Phys. B 859 (2012) 70 [arXiv:1112.3345] [INSPIRE].
A. Borghese, G. Dibitetto, A. Guarino, D. Roest and O. Varela, The SU(3)-invariant sector of new maximal supergravity, JHEP 03 (2013) 082 [arXiv:1211.5335] [INSPIRE].
G. Dibitetto, Gauged Supergravities and the Physics of Extra Dimensions, arXiv:1210.2301 [INSPIRE].
H. Samtleben and M. Weidner, The Maximal D = 7 supergravities, Nucl. Phys. B 725 (2005)383 [hep-th/0506237] [INSPIRE].
C.D.A. Blair and E. Malek, Geometry and fluxes of SL(5) exceptional field theory, JHEP 03 (2015) 144 [arXiv:1412.0635] [INSPIRE].
G. Aldazabal, E. Andres, P.G. Camara and M. Graña, U-dual fluxes and Generalized Geometry, JHEP 11 (2010) 083 [arXiv:1007.5509] [INSPIRE].
D. Andriot and A. Betz, β-supergravity: a ten-dimensional theory with non-geometric fluxes and its geometric framework, JHEP 12 (2013) 083 [arXiv:1306.4381] [INSPIRE].
D. Andriot and A. Betz, Supersymmetry with non-geometric fluxes, or a β-twist in Generalized Geometry and Dirac operator, JHEP 04 (2015) 006 [arXiv:1411.6640] [INSPIRE].
K. Lee, C. Strickland-Constable and D. Waldram, Spheres, generalised parallelisability and consistent truncations, arXiv:1401.3360 [INSPIRE].
R. Feger and T.W. Kephart, LieART - A Mathematica Application for Lie Algebras and Representation Theory, arXiv:1206.6379 [INSPIRE].
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Danielsson, U., Dibitetto, G. Geometric non-geometry. J. High Energ. Phys. 2015, 84 (2015). https://doi.org/10.1007/JHEP04(2015)084
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DOI: https://doi.org/10.1007/JHEP04(2015)084