Classification of supersymmetric flux vacua in M-theory

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 Kahler 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.