Jacobi sigma models

TL;DR

This paper introduces a new two-dimensional sigma model linked to Jacobi manifolds, extending Poisson sigma models, and explores its Hamiltonian structure and non-topological variants with metric and B-field.

Contribution

It presents the first formulation of a Jacobi sigma model, generalizing Poisson sigma models and connecting topological and non-topological string theories.

Findings

Derived first class constraints generating gauge invariance.

Reduced phase space is finite-dimensional.

Constructed a non-topological model with metric and B-field.

Abstract

We introduce a two-dimensional sigma model associated with a Jacobi manifold. The model is a generalisation of a Poisson sigma model providing a topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance of the model under diffeomorphisms. The reduced phase space is finite-dimensional. By introducing a metric tensor on the target, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold.