# Generalized $N$ = 1 and $N$ = 2 structures in M-theory and type II orientifolds

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Abstract : We consider M-theory and type IIA reductions to four dimensions with N = 2 and N = 1 supersymmetry and discuss their interconnection. Our work is based on the framework of Exceptional Generalized Geometry (EGG), which extends the tangent bundle to include all symmetries in M-theory and type II string theory, covariantizing the local U-duality group E 7(7). We describe general N = 1 and N = 2 reductions in terms of SU(7) and SU(6) structures on this bundle and thereby derive the effective four-dimensional N = 1 and N = 2 couplings, in particular we compute the Kähler and hyper-Kähler potentials as well as the triplet of Killing prepotentials (or the superpotential in the N = 1 case). These structures and couplings can be described in terms of forms on an eight-dimensional tangent space where SL(8) ⊂ E 7 acts, which might indicate a description in terms of an eight-dimensional internal space, similar to F-theory. We finally discuss an orbifold action in M-theory and its reduction to O6 orientifolds, and show how the projection on the N = 2 structures selects the N = 1 ones. We briefly comment on new orientifold projections, U-dual to the standard ones.
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Journal articles

Cited literature [15 references]

https://hal-cea.archives-ouvertes.fr/cea-00843124
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### Citation

Graña Mariana, Hagen Triendl. Generalized $N$ = 1 and $N$ = 2 structures in M-theory and type II orientifolds. Journal of High Energy Physics, Springer, 2013, pp.145. ⟨10.1007/JHEP03(2013)145⟩. ⟨cea-00843124⟩

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