SU(2|2) supersymmetric mechanics

Superfield approach to higher derivative $$ \mathcal{N} $$ = 1 superconformal mechanics

“…• find so(d)-invariant solutions of the equation (16) in terms of the rotationally invariant combinations;…”

“…Here and what follows we denote constants of the motion by the same letters which were used for designating the corresponding symmetry generators, but in a calligraphic style. As was mentioned above, in general, the superpotential for the fourth-order osp(2|1)invariant superconformal mechanics is a function of P (n) ij with n = 0, 1, 2, 3, which obeys the equation (16). The polynomials P (0) ij and P (1) ij are the same as in (17), but others are given by…”

“…In the next section we will consider a few examples of such superconformal mechanics. Let us consider a way to obtain so(d)-invariant solutions of the equation (16) for the case of l = 1 2 . In accord with (12), a rotationally invariant potential function V may depend on any scalars which can be constructed from the polynomials…”

“…as independent variables on which the potential function V depends. In this case the equation (16) can be rewritten as…”

Gauged spinning models with deformed supersymmetry

“…This SU(2|1) harmonic approach, as a deformation of the analogous formalism in N = 4 supersymmetric mechanics [9], have provided additional opportunities to build new SU(2|1) models, in particular those associated with the multiplet (4, 4, 0) and its "mirror" counterpart. As was pointed out in [1,2,3] (see also [10]), many issues of N = 4 supersymmetric mechanics still await their SU(2|1) generalization. The list includes the N = 4 supersymmetric Calogerolike systems, the gauging procedure in superspace, coupling to the background gauge fields, etc.…”