Brane wrapping, AKSZ sigma models, and QP manifolds

TL;DR

This paper develops a new method to implement brane wrapping and dimensional reduction within AKSZ topological sigma models and their symplectic QP-manifold targets, revealing novel relations between geometric structures.

Contribution

It introduces a coisotropic reduction combined with AKSZ transgression to realize brane wrapping in topological models, connecting flux rules and geometric structures.

Findings

Validated the procedure against known flux rules in M-theory/type IIA duality

Discovered a new relation between Courant algebroids and Poisson manifolds

Provided a framework for degree-shifting in AKSZ models

Abstract

We introduce a technique to realise brane wrapping and double dimensional reduction in the context of AKSZ topological sigma models and also in their target spaces, which are symplectic $L_n$-algebroids (i.e. QP-manifolds). Our procedure involves a novel coisotropic reduction combined with an AKSZ transgression that realises degree-shifting; the reduced QP-manifold depends on topological data of the `wrapped' cycle. We check our procedure against the known rules for fluxes under wrapping in the context of M-theory/type IIA duality, and we also find a new relation between Courant algebroids and Poisson manifolds.