$\mathcal{N}=4$ supersymmetric multiparticle systems based on indecomposable multiplets

Abstract

We construct new multiparticle models of $\mathcal{N}=4$ supersymmetric mechanics with spin degrees of freedom by employing nonlinear indecomposable supermultiplets $(1,4,3)\supset +(4,4,0)$. These systems are proper deformations of those associated with the standard irreducible $d=1$, $\mathcal{N}=4$ multiplets. In this way we find a deformation of $\mathcal{N}=4$ supersymmetric U$(2)$-spin rational Calogero system invariant under $d=1$ superconformal group OSp$(4|2)$. One more deformed model reproduces $\mathcal{N}=4$ supersymmetric U$(2)$-spin hyperbolic Calogero system, up to a shift of the Hamiltonian by some U$(1)$ generators.

1+25 pages; v3: revised version, references added, typos corrected