PT deformation of angular Calogero models

authored by

Francisco Correa, Olaf Lechtenfeld

Abstract

The rational Calogero model based on an arbitrary rank-n Coxeter root system is spherically reduced to a superintegrable angular model of a particle moving on Sⁿ⁻¹ subject to a very particular potential singular at the reflection hyperplanes. It is outlined how to find conserved charges and to construct intertwining operators. We deform these models in a PT-symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The PT deformation does not change the energy eigenvalues but in some cases adds a previously unphysical tower of states. For integral couplings the new and old energy levels coincide, which roughly doubles the previous degeneracy and allows for a conserved nonlinear supersymmetry charge. We present the details for the generic rank-two (A₂, G₂) and all rank-three Coxeter systems (AD₃, BC₃ and H₃), including a reducible case (A₁ ^{⊗ 3}).

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

Universidad Austral de Chile

Type

Artikel

Journal

Journal of high energy physics

Volume

2017

ISSN

1126-6708

Publication date

01.11.2017

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.1007/JHEP11(2017)122 (Access: Offen)