P T $$ \mathcal{P}\mathcal{T} $$ deformation of Calogero-Sutherland models

Abstract

Abstract Calogero-Sutherland models of N identical particles on a circle are deformed away from hermiticity but retaining a P T $$ \mathcal{P}\mathcal{T} $$ 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 A 2 and G 2.

Keywords

• Global Symmetries
• Integrable Field Theories
• Field Theories in Lower Dimensions
• Integrable Hierarchies