Bulg. J. Phys. vol.41 no.2 (2014), pp. 109-122

A Generalization of Calabi-Yau Fourfolds Arising from M-Theory Compactifications

E.M. Babalic1,2, C.I. Lazaroiu3
1Department of Physics, University of Craiova, 13 Al.~I. Cuza Str., Craiova 200585, Romania
2Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Str. Reactorului no.30, P.O.BOX MG-6, Bucharest-Magurele 077125, Romania
3Center for Geometry and Physics, Institute for Basic Science (IBS), 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, Korea 790-784
Abstract. Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising fom Fierz identities and from the differential and algebraic conditions on the internal part of the supersymmetry generators. The result makes use of the formulation of such problems through Kähler-Atiyah bundles, which we developed in previous work. Applying this to the most general N = 2 flux compactifications of 11-dimensional supergravity on 8-manifolds, we can extract the conditions constraining such backgrounds and give an overview of the resulting geometry, which generalizes that of Calabi-Yau fourfolds.

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