Topological Membranes with 3-Form H Flux on Generalized Geometries

TL;DR

This paper develops topological membrane and string models incorporating 3-form fluxes within generalized geometries, using AKSZ formalism, and explores their consistency conditions and structures.

Contribution

It introduces new topological models with nontrivial 3-form fluxes on generalized geometries using AKSZ formalism, extending previous frameworks.

Findings

Models realize Bianchi identities with nontrivial H flux

Constructed models for generalized SU(3), G2, and Spin(7) structures

Framework ensures consistency of flux backgrounds in topological theories

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 $G_2$ structure and a generalized $Spin(7)$ structure. These models are constructed from the AKSZ formulation of Batalin-Vilkovisky formalism.