TY - JOUR

T1 - PT deformation of angular Calogero models

AU - Correa, Francisco

AU - Lechtenfeld, Olaf

N1 - Funding Information: Open Access, ©c The Authors. Article funded by SCOAP3. Funding Information: This work was partially supported by the Alexander von Humboldt Foundation under grant CHL 1153844 STP and by the Deutsche Forschungsgemeinschaft under grant LE 838/12. This article is based upon work from COST Action MP1405 QSPACE, supported by COST (European Cooperation in Science and Technology). F.C. is grateful for the warm hospitality at Leibniz Universität Hannover, where the main part of this work was done. Publisher Copyright: © 2017, The Author(s). Copyright: Copyright 2017 Elsevier B.V., All rights reserved. Publisher Copyright: © 2017, The Author(s).

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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).

AB - 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).

KW - Conformal and W Symmetry

KW - Discrete Symmetries

KW - Field Theories in Lower Dimensions

KW - Integrable Field Theories

UR - http://www.scopus.com/inward/record.url?scp=85036565993&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2017)122

DO - 10.1007/JHEP11(2017)122

M3 - Article

AN - SCOPUS:85036565993

VL - 2017

JO - Journal of high energy physics

JF - Journal of high energy physics

SN - 1126-6708

IS - 11

M1 - 122

ER -