## Topological membranes with 3-form $$H$$ flux on generalized geometries.(English)Zbl 1151.81035

Summary: 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 $$G_{2}$$ structure and a generalized Spin(7) structure. These models are constructed from the AKSZ formulation of the Batalin-Vilkovisky formalism.

### MSC:

 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 83E30 String and superstring theories in gravitational theory 22E70 Applications of Lie groups to the sciences; explicit representations
Full Text: