### T-duality and Double Sigma Models

After discussing some proposals for a manifestly T-dual invariant string world-sheet, the notion of Poisson-Lie T-duality will be introduced together with the one of Drinfeld double that constitutes the algebraic structure necessary for the existence of such duality . As an illustrating example, a simple mechanical system, the three-dimensional isotropic rigid rotator, will be investigated as a 0+1 field theory, aiming at understanding how such duality works and how it is related to Generalized Geometry. The model is defined over the group manifold of SU(2) and its dual is introduced having the Poisson-Lie dual of SU(2) as configuration space. A “double" generalized action with configuration space SL(2,C), i.e. the Drinfeld double of SU(2), is then defined containing twice as many variables as the original. It reduces to the original action or to its dual, once constraints are suitably implemented. Furthermore, the geometric structures of this double action can be understood in terms of Generalized Geometry. The case of Principal Chiral Model will be also briefly illustrated.

**Tuesday, 27 November 2018, 14:30, Aula Wataghin**