Brane wrapping, Alexandrov-Kontsevich-Schwarz-Zaboronsky sigma models, and QP manifolds

We introduce a technique to realize brane wrapping and double dimensional reduction in the context of Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) topological sigma models and also in their target spaces, which are symplectic Ln algebroids (i.e., QP manifolds). Our procedure involves a novel coisotropic reduction combined with an AKSZ transgression that realizes 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.

Automated summary

This study introduces a new technique to achieve brane wrapping and double dimensional reduction in the AKSZ topological sigma models, and discovers a new relation between two manifolds.