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arXiv · 1802.04581

AKSZ constructions for topological membranes on $G_2$-manifolds

Zoltan Kokenyesi·Annamaria Sinkovics·Richard J. Szabo
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Abstract

We 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 $G_2$-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.

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Zoltan Kokenyesi, Annamaria Sinkovics, Richard J. Szabo. 2018-03-07. AKSZ constructions for topological membranes on $G_2$-manifolds. https://doi.org/10.1002/prop.201800018

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