Topological membranes with 3-form $H$ flux on generalized geometries

Abstract

We construct topological string and topological membrane actions with a nontrivial 3-form flux $H$ in arbitrary dimensions. These models realize Bianchi identities with a nontrivial $H$ flux as consistency conditions. Especially, we discuss the models with a generalized $SU(3)$ structure, a generalized G₂ structure and a generalized Spin(7) structure. These models are constructed from the AKSZ formulation of the Batalin–Vilkovisky formalism.