A Simple Model for Non-Abelian T-duality and Double Field Theory

A simple mechanical system, the rigid rotator, is here investigated as a 0+1 field theory, aiming at further investigating the relation between Generalized Geometry and Double Field Theory. The model is defined over the group manifold of SU(2). A dual model is then introduced having the Poisson-Lie dual of SU(2) as configuration space. The dynamics of both models possesses Poisson-Lie symmetries, which are made manifest by introducing an alternative action functional. This latter reduces to the ordinary one, once constraints are implemented. The new action contains twice as many variables as the original, as is also seen in Double Field Theory. Moreover its geometric structures can be understood in terms of Generalized Geometry.