Poly-symplectic geometry and the AKSZ formalism

Author:

Contreras Ivan1ORCID,Martínez Alba Nicolás2

Affiliation:

1. Department of Mathematics and Statistics, Amherst College, 31 Quadranlge Drive, Amhertst, MA 01002, USA

2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional de Colombia, Sede Bogotá, Carrera 45 No. 26-85, Bogotá 111321, Colombia

Abstract

In this paper, 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

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