# ${\cal PT}$ deformation of Calogero-Sutherland models

## TL;DR

This paper explores a non-Hermitian, yet $ ext{PT}$-symmetric deformation of Calogero-Sutherland models, revealing regularized potentials, extended spectra, and preserved integrability with new supersymmetry features.

## Contribution

It introduces a $ ext{PT}$-symmetric deformation of Calogero-Sutherland models that regularizes the potential and maintains integrability, while uncovering new supersymmetry and spectral properties.

## Key findings

- Regularized interaction potential with $ ext{PT}$ symmetry.
- Infinite tower of non-normalizable states becomes normalizable.
- Enhanced degeneracy and supersymmetry at integral couplings.

## Abstract

Calogero-Sutherland models of $N$ identical particles on a circle are deformed away from hermiticity but retaining a $\cal PT$ 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 $A_2$ and $G_2$.