N=1 geometries for M-theory and type IIA strings with fluxes

Details N=1 geometries for M-theory and type IIA strings with fluxes N=1 geometries for M-theory and type IIA strings with fluxes

2003-11-17

arxiv.org/abs/hep-th/0311146v3

Phys.Rev. D69 (2004) 066004

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, typos corrected, comments and references added, final version to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.69.066004

We derive a set of necessary and sufficient conditions for obtaining N=1 backgrounds of M-theory and type IIA strings in the presence of fluxes. Our metrics are warped products of four-dimensional Minkowski space-time with a curved internal manifold. We classify the different solutions for irreducible internal manifolds as well as for manifolds with $S^1$ isometries by employing the formalism of group structures and intrinsic torsion. We provide examples within these various classes along with general techniques for their construction. In particular, we generalize the Hitchin flow equations so that one can explicitly build irreducible 7-manifolds with 4-form flux. We also show how several of the examples found in the literature fit in our framework and suggest possible generalizations.

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