Classical boundary field theory of Jacobi sigma models by Poissonization

TL;DR

This paper develops a classical boundary field theory for Jacobi sigma models using poissonization, extending methods from Poisson sigma models and providing explicit perturbative field expansions up to second order.

Contribution

It introduces a novel boundary field theory for Jacobi sigma models via poissonization, generalizing existing techniques from Poisson sigma models.

Findings

Fields expressed as perturbative expansions in boundary phase space

Explicit calculations of fields up to second order

Application example for contact manifolds

Abstract

In this paper, we are going to construct the classical field theory on the boundary of the embedding of $\mathbb{R} \times S^{1}$ into the manifold $M$ by the Jacobi sigma model. By applying the poissonization procedure and by generalizing the known method for Poisson sigma models, we express the fields of the model as perturbative expansions in terms of the reduced phase space of the boundary. We calculate these fields up to the second order and illustrate the procedure for contact manifolds.