# Poly-Poisson Sigma models and their relational poly-symplectic groupoids

## TL;DR

This paper develops a method to integrate poly-Poisson structures into poly-symplectic groupoids using topological field theories and path-space constructions, extending previous results.

## Contribution

It introduces a new integration procedure for poly-Poisson structures via relational poly-symplectic groupoids using the poly-Poisson sigma model.

## Key findings

- Every poly-Poisson structure admits a natural integration.
- Provides examples including trivial, linear, constant, and symplectic cases.
- Applications include classification of poly-symplectic integrations and Morita equivalence.

## Abstract

The main idea of this note is to describe the integration procedure for poly-Poisson structures, that is, to find a poly-symplectic groupoid integrating a poly-Poisson structure, in terms of topological field theories, namely via the path-space construction. This will be given in terms of the poly-Poisson sigma model $(PPSM)$ and we prove that every poly-Poisson structure has a natural integration via relational poly-symplectic groupoids, extending the results in [8] and [26]. We provide familiar examples (trivial, linear, constant and symplectic) within this formulation and we give some applications of this construction regarding the classification of poly-symplectic integrations, as well as Morita equivalence of poly-Poisson manifolds.