New realizations of the supergroup D(2, 1; α) in N = 4 $$ \mathcal{N}=4 $$ superconformal mechanics

Abstract

We present new explicit realizations of the most general $$ \mathcal{N}=4 $$ , d = 1 superconformal symmetry D(2, 1; α) in the models of $$ \mathcal{N}=4 $$ superconformal mechanics based on the reducible multiplets (1 , 4 , 3) ⊕ (0 , 4 , 4), (3 , 4 , 1) ⊕ (0 , 4 , 4) and (4 , 4 , 0) ⊕ (0 , 4 , 4). We start from the manifestly supersymmetric superfield actions for these systems and then descend to the relevant off- and on-shell component actions from which we derive the D(2, 1; α) (super)charges by the Noether procedure. Some peculiarities of these realizations of D(2, 1; α) are discussed. We also construct a new D(2, 1; α) invariant system by joining the multiplets (3 , 4 , 1) and (4 , 4 , 0) in such a way that they interact with each other through an extra (0 , 4 , 4) multiplet. New fermionic conformal couplings appear as the result of elimination of the appropriate auxiliary fields.