Couplings of $\mathcal{N}=4$, $d=1$ mirror supermultiplets

Abstract

We construct models of coupled semi-dynamical (spin) and dynamical mirror multiplets of $\mathcal{N}=4$ supersymmetric mechanics in $d=1$ harmonic superspace. Specifically, we consider a semi-dynamical mirror multiplet $(3,4,1)$ coupled to dynamical mirror multiplets $(1,4,3)$ and $(2,4,2)$. Coupling of the multiplets $(3,4,1)$ and $(1,4,3)$ yields a mirror counterpart of the earlier constructed model implying the Nahm equations for the spin variables with the bosonic component of the multiplet $(1,4,3)$ as an evolution parameter. We also couple the mirror multiplet $(2,4,2)$ to the mirror semi-dynamical multiplet $(3,4,1)$ using chiral $\mathcal{N}=4$ superspace. The models constructed admit a generalization to the SU$(2|1)$ deformation of $\mathcal{N}=4$, $d=1$ Poincaré supersymmetry.

1+18 pages, appendix added and some other minor changes, published version