Supersymmetric Calogero models by gauging

Abstract

New superconformal extensions of $d=1$ Calogero-type systems are obtained by gauging the $\mathrm{U}(n)$ isometry of matrix superfield models. We consider the cases of $\mathcal{N}=1$, $\mathcal{N}=2$, and $\mathcal{N}=4$ as one-dimensional supersymmetries. The bosonic core of the $\mathcal{N}=1$ and $\mathcal{N}=2$ models is the standard conformal ${A}_{n\ensuremath{-}1}$ Calogero system, whereas the $\mathcal{N}=4$ model is an extension of the U(2)-spin Calogero system.