AKSZ Constructions for Topological Membranes on G2‐Manifolds

Abstract

AbstractWe consider AKSZ constructions of BV actions for closed topological membranes, and their dimensional reductions to topological string sigma‐models. Two inequivalent AKSZ constructions for topological membranes on G2‐manifolds are proposed, in each of which the two existing topological membrane theories appear as different gauge fixed versions. Their dimensional reductions give new AKSZ constructions for the topological A‐model, which on further dimensional reduction gives an AKSZ formulation of supersymmetric quantum mechanics. We show that the two AKSZ membrane models originate through worldvolume dimensional reduction of a single AKSZ threebrane theory, which gives the standard 2‐Courant bracket as the underlying derived bracket. Double dimensional reduction of the twisted topological threebrane theory on a circle yields the standard Courant sigma‐model for string theory with NS–NS flux.