Poly-symplectic Geometry and the AKSZ Formalism

TL;DR

This paper extends the AKSZ formalism to poly-symplectic and poly-Poisson structures, developing graded geometry theory and applying it to the poly-Poisson sigma model's phase space.

Contribution

It introduces a generalized AKSZ framework for poly-symplectic geometry and proves foundational theorems like Schwarz-type and transgression results.

Findings

Established a generalized AKSZ formulation for poly-symplectic structures.

Proved a Schwarz-type theorem and transgression for graded poly-symplectic structures.

Recovered the action functional and phase space structure of the poly-Poisson sigma model.

Abstract

We extend the AKSZ formulation of the Poisson sigma model to more general target spaces, and we develop the general theory of graded geometry for poly-symplectic and poly-Poisson structures. In particular we prove a Schwarz-type theorem and transgression for graded poly-symplectic structures, recovering the action functional and the poly-symplectic structure of the reduced phase space of the poly-Poisson sigma model, from the AKSZ construction.