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 \( \mathcal{P}\mathcal{T} \)-symmetric manner by judicious complex coordinate transformations, which render the potential less singular. The \( \mathcal{P}\mathcal{T} \) 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 (A2, G2) and all rank-three Coxeter systems (AD3, BC3 and H3), including a reducible case (A ⊗ 31 ).
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Correa, F., Lechtenfeld, O. \( \mathcal{P}\mathcal{T} \) deformation of angular Calogero models. J. High Energ. Phys. 2017, 122 (2017). https://doi.org/10.1007/JHEP11(2017)122
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DOI: https://doi.org/10.1007/JHEP11(2017)122