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

Abstract

Calogero-Sutherland models of $N$ identical particles on a circle are deformed away from hermiticity but retaining a $\mathcal{P}\mathcal{T}$ 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 $G_2$.

arXiv comment1+21 pages; v2: one reference added, minor corrections and improvements, matches published version

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Cited by in corpus (5)

• Polynomial algebras from $su(3)$ and the generic model on the two sphere
• Integrability, intertwiners and non-linear algebras in Calogero models
• A route from maximal chaoticity to integrability
• Coupling and particle number intertwiners in the Calogero model
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry