Gauging N=4N=4 supersymmetric mechanics II: (1,4,3)(1,4,3) models from the (4,4,0)(4,4,0) ones

Exploiting the gauging procedure developed by us in hep-th/0605211, we study the relationships between the models of N=4N=4 mechanics based on the off-shell multiplets (4,4,0)(4,4,0) and (1,4,3)(1,4,3). We make use of the off-shell N=4N=4, d=1d=1 harmonic superspace approach as most adequate for treating this circle of problems. We show that the most general sigma-model type superfield action of the multiplet (1,4,3)(1,4,3) can be obtained in a few non-equivalent ways from the (4,4,0)(4,4,0) actions invariant under certain three-parameter symmetries, through gauging the latter by the appropriate non-propagating gauge multiplets. We discuss in detail the gauging of both the Pauli–Gürsey SU(2)SU(2) symmetry and the Abelian three-generator shift symmetry. We reveal the (4,4,0)(4,4,0) origin of the known mechanisms of generating potential terms for the multiplet (1,4,3)(1,4,3), as well as of its superconformal properties. A new description of this multiplet in terms of unconstrained harmonic analytic gauge superfield is proposed. It suggests, in particular, a novel mechanism of generating the (1,4,3)(1,4,3) potential terms via coupling to the fermionic off-shell N=4N=4 multiplet (0,4,4)(0,4,4).