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Classification of Supersymmetric Flux Vacua in M Theory

Klaus Behrndt·Mirjam Cvetic·Tao Liu
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Abstract

We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2 structures. In particular, we find for N = 2 supersymmetry, that the external space-time is Minkowski and the base manifold of the internal space is conformally Kähler for SU(2) structures, while for SU(3) structures the internal space has to be Einstein-Sasaki and no internal fluxes are allowed. Moreover, we provide a new vacuum with N = 1 supersymmetry and SU(3) structure, where all fluxes are non-zero and the first order differential equations are solved.

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Klaus Behrndt, Mirjam Cvetic, Tao Liu. 2006-04-25. Classification of Supersymmetric Flux Vacua in M Theory. https://doi.org/10.1016/j.nuclphysb.2006.04.018

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