AKSZ construction from reduction data

TL;DR

This paper presents a general method to incorporate target space reductions into AKSZ sigma models using BFV models, with examples illustrating the approach in low dimensions.

Contribution

It introduces a systematic procedure to encode target space reduction within AKSZ models via BFV models, connecting with existing models in the literature.

Findings

Established a general reduction procedure for AKSZ models

Connected AKSZ models with BFV models for constrained spaces

Recovered known models in 2D and 3D cases

Abstract

We discuss a general procedure to encode the reduction of the target space geometry into AKSZ sigma models. This is done by considering the AKSZ construction with target the BFV model for constrained graded symplectic manifolds. We investigate the relation between this sigma model and the one with the reduced structure. We also discuss several examples in dimension two and three when the symmetries come from Lie group actions and systematically recover models already proposed in the literature.