PT $$ \ cal{T} $$ deformation of angular Calogero models

• Published in: The journal of high energy physics Vol. 2017; no. 11; pp. 1 - 44
• Main Authors: Francisco Correa, Olaf Lechtenfeld
• Format: Journal Article
• Language: English
• Published: SpringerOpen 01.11.2017
• Subjects: Conformal and W Symmetry; Discrete Symmetries; Field Theories in Lower Dimensions; Integrable Field Theories
• ISSN: 1029-8479
• DOI: 10.1007/JHEP11(2017)122

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 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 PT $$ \mathcal{P}\mathcal{T} $$-symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The PT $$ \mathcal{P}\mathcal{T} $$ 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).