Graded Contact Geometry and the AKSZ Formalism

TL;DR

This paper extends the AKSZ formalism to differential graded contact manifolds, leading to new topological field theories and generalizing known models like the Jacobi sigma model.

Contribution

It introduces a graded contact geometry framework within the AKSZ formalism, constructing solutions to the master equation using Jacobi brackets.

Findings

Recovered the Jacobi sigma model for n=1

Derived 3D topological theories from Courant-Jacobi algebroids

Established a weak contact structure on the space of fields

Abstract

The AKSZ formalism is a construction of topological field theories where the target spaces are differential graded symplectic manifolds. In this paper, we describe an analogue of the AKSZ formalism where the target spaces are differential graded contact manifolds. We show that the space of fields inherits a weak contact structure, and we construct a solution to the analogue of the classical master equation, defined via the Jacobi bracket. In the $n=1$ case, we recover the Jacobi sigma model, and in the $n=2$ case, we obtain three-dimensional topological field theories associated to Courant-Jacobi algebroids.