Finite dimensional AKSZ-BV theories

TL;DR

This paper introduces a method to reduce AKSZ-BV theories to finite dimensions by focusing on source manifold cohomology, enabling explicit computation of correlators and extending the AKSZ framework.

Contribution

It presents a canonical reduction technique for AKSZ-BV theories to finite dimensions using source cohomology, with applications to specific sigma models and potential generalizations.

Findings

Finite dimensional BV theories describe zero mode contributions.

Integration and correlator computation are feasible in the reduced theories.

The approach generalizes AKSZ construction using source cohomology.

Abstract

We describe a canonical reduction of AKSZ-BV theories to the cohomology of the source manifold. We get a finite dimensional BV theory that describes the contribution of the zero modes to the full QFT. Integration can be defined and correlators can be computed. As an illustration of the general construction we consider two dimensional Poisson sigma model and three dimensional Courant sigma model. When the source manifold is compact, the reduced theory is a generalization of the AKSZ construction where we take as source the cohomology ring. We present the possible generalizations of the AKSZ theory.