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.
Highlights
This consists of supplementing the action of the Jacobi sigma model with a dynamical term which includes a metric tensor on the target space
We will show that there is an ::::::: review ::: the:almost one-to-one correIn this section, we review the almost one-to-one correspondence between the Jacobi spondence between the Jacobi sigma model described in the previous sections and the sigma model described in the previous sections and the reduced model which may be reduced model which may be obtained on the Jacobi manifold after Poissonisation
The Jacobi sigma model is a generalisation of the well known Poisson sigma model. It is a two-dimensional topological non-linear gauge theory describing strings moving on a Jacobi background
Summary
It makes it possible to unravel mathematical aspects of such manifolds by employing techniques from field theory An example of this relation was given by Cattaneo and Felder in [4,5] where they show that the reduced phase space of the Poisson sigma model is the symplectic groupoid integrating the Lie algebroid associated with the Poisson structure of the target manifold. This consists of supplementing the action of the Jacobi sigma model with a dynamical term which includes a metric tensor on the target space. We conclude with a final discussion of the results with remarks and perspectives
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