A novel multi-parameter family of quantum systems with partially broken N-fold supersymmetry

Abstract

We develop a systematic algorithm for constructing an X-fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we construct a new multiparameter family of Ar-fold supersymmetric models, which shall be referred to as 'type C'. We investigate various aspects of these type C models in detail. It turns out that in certain cases these systems exhibit a novel phenomenon, namely, partial breaking of M-fold supersymmetry.