T-Dualities and Doubled Geometry of the Principal Chiral Model

Understand

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized and Doubled Geometry.

• A one-parameter family of equivalent Hamiltonian descriptions is introduced, and cast into the form of Born geometries.
• Then O(3,3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2,C) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel'd double SL(2, C).
• Moreover, starting from the Lagrangian approach, a new kind of duality is found between the SU(2) PCM and the natural one defined on SB(2,C) which is not an isometry of the target phase space.