  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.
