Couplings in D(2,1;a) superconformal mechanics from the SU(2) perspective

Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;a) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some phase space can be extended to a representation of the Lie superalgebra corresponding to D(2,1;a). Novel couplings of arbitrary number of supermultiplets of the type (1,4,3) and (0,4,4) with a single supermultiplet of either the type (3,4,1), or (4,4,0) are constructed. D(2,1;a) superconformal mechanics describing superparticles propagating near the horizon of the extreme Reissner-Nordstrom-AdS-dS black hole in four and five dimensions is considered. The parameter a is linked to the cosmological constant.