Extended supersymmetric Calogero model

Abstract

We present a surprising redefinition of matrix fermions which brings the supercharges of the N-extended supersymmetric An−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 A2n−1⊕A1 to explicitly construct the supercharges and Hamiltonian for arbitrary even-N supersymmetric extensions of the Bn, Cn and Dn rational Calogero models. We demonstrate that all considered models possess a dynamical osp(N|2) superconformal symmetry. Keywords: Calogero models, Extended supersymmetry