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Starting from a higher Courant bracket associated to exceptional generalizedgeometry, we provide a systematic derivation of all types of fluxes and theirBianchi identities for four-dimensional compactifications of M-theory. We showthat these fluxes may be understood as generalized Wess-Zumino terms in certaintopological threebrane sigma-models of AKSZ-type, which relates them to thehigher structure of a Lie algebroid up to homotopy. This includes geometriccompactifications of M-theory with G-flux and on twisted tori, and also itscompactifications with non-geometric Q- and R-fluxes in specificrepresentations of the U-duality group SL(5) in exceptional field theory.

Fluxes in Exceptional Field Theory and Threebrane Sigma-Models