Topological and Dynamical Aspects of Jacobi Sigma Models

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.

T-dualities and Doubled Geometry of the Principal Chiral Model

“…A further extension of this model can be given adding a Wess-Zumino term [97]. This could provide a deeper insight, among other things, on the geometric structures of String Theory on AdS 3 , the study of which is interesting from the point of view of the AdS/CF T correspondence since it enables to study the correspondence beyond the gravity approximation [98,99,100].…”

T-Duality and Doubling of the Isotropic Rigid Rotator

“…The isotropic rigid rotator is a toy model, representing a sigma model in 0 + 1 dimensions. Its true field theory generalization, which is the Principal Chiral Model, is presented in [56]; the inclusion into the latter of a Wess-Zumino term is currently under investigation [57]. Besides being interesting per se, these models may contribute to a better understanding of the string world-sheet formulation, with the possibility of writing a manifestly O(d, d) T-duality invariant doubled action in a more rigorous way and then performing the low energy limit where all the results obtained in Double Field Theory should be recovered.…”

“…The model is simple but nonetheless it can give precious information, especially in view of its direct true field theory generalization that is the principal chiral model, analysed in [56] having this simple model as a guide. This is not the only generalization whose dynamics can be captured by the rotator, such as the Wess-Zumino-Witten model (whose results are going to be detailed in a forthcoming paper [57] or (2 + 1)-dimensional gravity in its first order formulation [58] among many others.…”