Abstract
We investigate M-theory and heterotic compactifications to 7 and 3 dimensions. In 7 dimensions we discuss a class of massive supergravities that arise from M-theory on K3 and point out obstructions to realizing these theories in a dual heterotic framework with a geometric description. Taking M-theory further down to 3 dimensions on K3 × K3 with a choice of flux leads to a rich landscape of theories with various amounts of supersymmetry, including those preserving 6 supercharges. We explore possible heterotic realizations of these vacua and prove a no-go theorem: every heterotic geometry that preserves 6 supercharges preserves 8 supercharges.
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References
E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP 08 (1999) 023 [hep-th/9908088] [INSPIRE].
K. Becker, M. Becker, J.-X. Fu, L.-S. Tseng and S.-T. Yau, Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory, Nucl. Phys. B 751 (2006) 108 [hep-th/0604137] [INSPIRE].
K. Becker and S. Sethi, Torsional heterotic geometries, Nucl. Phys. B 820 (2009) 1 [arXiv:0903.3769] [INSPIRE].
I.V. Melnikov, R. Minasian and S. Theisen, Heterotic flux backgrounds and their IIA duals, JHEP 07 (2014) 023 [arXiv:1206.1417] [INSPIRE].
I.V. Melnikov, R. Minasian and S. Sethi, Heterotic fluxes and supersymmetry, JHEP 06 (2014) 174 [arXiv:1403.4298] [INSPIRE].
D.D. Joyce, Compact manifolds with special holonomy, Oxford Mathematical Monographs, Oxford University Press, Oxford U.K., (2000).
I.V. Lavrinenko, H. Lü and C.N. Pope, From topology to generalized dimensional reduction, Nucl. Phys. B 492 (1997) 278 [hep-th/9611134] [INSPIRE].
H. Lü and C.N. Pope, Domain walls from M-branes, Mod. Phys. Lett. A 12 (1997) 1087 [hep-th/9611079] [INSPIRE].
N. Kaloper and R.C. Myers, The O(dd) story of massive supergravity, JHEP 05 (1999) 010 [hep-th/9901045] [INSPIRE].
R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, Non-geometric fluxes, asymmetric strings and nonassociative geometry, J. Phys. A 44 (2011) 385401 [arXiv:1106.0316] [INSPIRE].
A. Sen, Orientifold limit of F-theory vacua, Phys. Rev. D 55 (1997) R7345 [hep-th/9702165] [INSPIRE].
L.J. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett. 169B (1986) 374 [INSPIRE].
C.M. Hull, Massive string theories from M-theory and F-theory, JHEP 11 (1998) 027 [hep-th/9811021] [INSPIRE].
J. McOrist, D.R. Morrison and S. Sethi, Geometries, non-geometries and fluxes, Adv. Theor. Math. Phys. 14 (2010) 1515 [arXiv:1004.5447] [INSPIRE].
I. García-Etxebarria, D. Lüst, S. Massai and C. Mayrhofer, Ubiquity of non-geometry in heterotic compactifications, JHEP 03 (2017) 046 [arXiv:1611.10291] [INSPIRE].
P.M. Cowdall, H. Lü, C.N. Pope, K.S. Stelle and P.K. Townsend, Domain walls in massive supergravities, Nucl. Phys. B 486 (1997) 49 [hep-th/9608173] [INSPIRE].
E. Witten, On flux quantization in M-theory and the effective action, J. Geom. Phys. 22 (1997) 1 [hep-th/9609122] [INSPIRE].
M.J. Duff, J.T. Liu and R. Minasian, Eleven-dimensional origin of string-string duality: a one loop test, Nucl. Phys. B 452 (1995) 261 [hep-th/9506126] [INSPIRE].
K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].
B.S. Acharya, X. de la Ossa and S. Gukov, G flux, supersymmetry and Spin(7) manifolds, JHEP 09 (2002) 047 [hep-th/0201227] [INSPIRE].
P.S. Aspinwall, An analysis of fluxes by duality, hep-th/0504036 [INSPIRE].
D. Prins and D. Tsimpis, Type IIA supergravity and M-theory on manifolds with SU(4) structure, Phys. Rev. D 89 (2014) 064030 [arXiv:1312.1692] [INSPIRE].
J.P. Gauntlett, D. Martelli and D. Waldram, Superstrings with intrinsic torsion, Phys. Rev. D 69 (2004) 086002 [hep-th/0302158] [INSPIRE].
D. Prins and D. Tsimpis, 3d N = 1 effective supergravity and F-theory from M-theory on fourfolds, JHEP 09 (2015) 107 [arXiv:1506.07356] [INSPIRE].
B. de Wit, A.K. Tollsten and H. Nicolai, Locally supersymmetric D = 3 nonlinear σ-models, Nucl. Phys. B 392 (1993) 3 [hep-th/9208074] [INSPIRE].
K. Becker, D. Robbins and E. Witten, The α′ expansion on a compact manifold of exceptional holonomy, JHEP 06 (2014) 051 [arXiv:1404.2460] [INSPIRE].
A. Strominger, Superstrings with torsion, Nucl. Phys. B 274 (1986) 253 [INSPIRE].
T. Friedrich and S. Ivanov, Killing spinor equations in dimension 7 and geometry of integrable G 2 manifolds, J. Geom. Phys. 48 (2003) 1 [math/0112201] [INSPIRE].
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].
T. Friedrich, I. Kath, A. Moroianu and U. Semmelmann, On nearly parallel G 2 -structures, J. Geom. Phys. 23 (1997) 259.
I.V. Melnikov, R. Minasian and S. Sethi, Spacetime supersymmetry in low-dimensional perturbative heterotic compactifications, arXiv:1707.04613 [INSPIRE].
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ArXiv ePrint: 1702.08537
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Melnikov, I.V., Minasian, R. & Sethi, S. Non-duality in three dimensions. J. High Energ. Phys. 2017, 53 (2017). https://doi.org/10.1007/JHEP10(2017)053
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DOI: https://doi.org/10.1007/JHEP10(2017)053