PT deformation of angular Calogero models

• Published in: The journal of high energy physics Vol. 2017; no. 11
• Main Authors: Correa, Francisco, Lechtenfeld, Olaf
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 20.11.2017
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Discrete Symmetries; Field Theories in Lower Dimensions; Integrable Field Theories; Conformal and W Symmetry
• ISSN: 1029-8479
• DOI: 10.1007/JHEP11(2017)122

A bstract 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 S n −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 P T -symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The P T 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 ( A 2 , G 2 ) and all rank-three Coxeter systems ( AD 3 , BC 3 and H 3 ), including a reducible case ( A 1 ⊗ 3 ).