Topological and dynamical aspects of Jacobi sigma models

TL;DR

This paper explores the geometric and dynamical properties of Jacobi sigma models, a class of topological field theories that generalize Poisson sigma models, focusing on their constraints, gauge symmetries, and specific manifold examples.

Contribution

It provides a detailed Hamiltonian analysis of Jacobi sigma models, highlighting their unique features and extending the understanding of topological field theories with Jacobi target spaces.

Findings

Jacobi sigma models exhibit gauge invariance under diffeomorphisms.

The models have a finite-dimensional reduced phase space.

Contact and locally conformal symplectic manifolds serve as key examples.

Abstract

The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories - recently introduced by the authors - which share and generalise relevant features of Poisson sigma models, such as gauge invariance under diffeomorphisms and finite dimension of the reduced phase space. After reviewing the main novelties and peculiarities of these models, we perform a detailed analysis of constraints and ensuing gauge symmetries in the Hamiltonian approach. Contact manifolds as well as locally conformal symplectic manifolds are discussed, as main instances of Jacobi manifolds.