AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

TL;DR

This paper explores the AKSZ-BV formalism within graded manifolds and constructs a 3D topological sigma-model from Courant algebroids, advancing the understanding of topological field theories.

Contribution

It provides a detailed exposition of the AKSZ-BV formalism and introduces a canonical 3D topological sigma-model associated with Courant algebroids.

Findings

Constructed the BV master action for the Courant algebroid-based model

Established a canonical association between Courant algebroids and topological sigma-models

Enhanced the mathematical framework for topological field theories

Abstract

We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a three-dimensional topological sigma-model. Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the model.