$PT$ deformation of Calogero-Sutherland models

Calogero-Sutherland models of N identical particles on a circle are deformed away from hermiticity but retaining a $PT$ symmetry. The interaction potential gets completely regularized, which adds to the energy spectrum an infinite tower of previously non-normalizable states. For integral values of the coupling, extra degeneracy occurs and a nonlinear conserved supersymmetry charge enlarges the ring of Liouville charges. The integrability structure is maintained. We discuss the A_{N −1}-type models in general and work out details for the cases of A₂ and G₂.