Orateur
Description
Double Field Theory can be formulated on a 2d-dimensional para-Hermitian manifold ($P,\eta,\omega$) by supplementing the $O(d,d)$ metric $\eta$ with an almost symplectic two-form $\omega$. Together $\eta$ and $\omega$ provide a bi-Lagrangian splitting of the tangent bundle TP into two Lagrangian subspaces. I will sketch how to construct a canonical connection and a corresponding generalized Lie derivative for the Leibniz algebroid on TP. Under certain integrability conditions the symmetry algebra closes for general $\eta$ and $\omega$, even when they are not flat and constant. This provides a generalization of the kinematical structure of DFT. By including the generalized metric $H$ into the setup - which thus becomes para-quaternionic - we can construct a connection compatible with all three structures ($\eta, \omega, H$) and thus can also generalize the dynamics. The precise relation between DFT and generalized geometry is also discussed.
