A toy model for Double Field Theory and its generalization to Principal Chiral Models

will discuss a double geometry formulation of the isotropic rigid rotator, as a dynamical system whose configuration space is usually chosen to be the group manifold of SU(2). I will generalize the carrier space of the dynamics in terms of the double group of SU(2) and discuss the emerging geometry. The construction is thus extended to principal chiral models as an instance of $1+1$ field theory with non-Abelian duality.