We study the most general supersymmetric warped M-theory backgrounds with a non-trivial G flux of the type R1,2×M₈ and AdS₃×M₈. We give a set of necessary and sufficient conditions for preservation of supersymmetry which are phrased in terms of G structures and their intrinsic torsion. These equations may be interpreted as calibration conditions for a static ``dyonic'' M-brane, that is, an M5-brane with a self-dual three-form turned on. When the electric flux is turned off we obtain the supersymmetry conditions and non-linear PDEs describing M5-branes wrapped on associative and special Lagrangian three-cycles in manifolds with G₂ and SU(3) structures, respectively. As an illustration of our formalism, we recover the 1/2 BPS dyonic M-brane, and also construct some new examples.
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Martelli et al. (2003) studied this question.
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