Extended supersymmetric Calogero model

Sergey Krivonos; Olaf Lechtenfeld; Alexander Provorov; Anton Sutulin

doi:10.1016/j.physletb.2019.03.004

paper

Extended supersymmetric Calogero model

arXiv:1812.10168 · doi:10.1016/j.physletb.2019.03.004

Abstract

We present a surprising redefinition of matrix fermions which brings the supercharges of the $N$ -extended supersymmetric $A_{n - 1}$ Calogero model introduced in [1] to the standard form maximally cubic in the fermions. The complexity of the model is transferred to a non-canonical and nonlinear conjugation property of the fermions. Employing the new cubic supercharges, we apply a supersymmetric generalization of a "folding" procedure for $A_{2 n - 1} \oplus A_{1}$ to explicitly construct the supercharges and Hamiltonian for arbitrary even- $N$ supersymmetric extensions of the $B_{n}$ , $C_{n}$ and $D_{n}$ rational Calogero models. We demonstrate that all considered models possess a dynamical $os p (N ∣2)$ superconformal symmetry.

1+7 pages; v2: more precise citations, one ref. added, version appearing in PLB