Supersymmetric hyperbolic Calogero-Sutherland models by gauging

Novel $\mathcal{N}=2$ and $\mathcal{N}=4$ supersymmetric extensions of the Calogero-Sutherland hyperbolic systems are obtained by gauging the ${\rm U}(n)$isometryofmatrixsuperfieldmodels\mathrm{.}Thebosoniccoreofthe$$\mathcal{N}${=},2$modelsisthestandard$A_{n-1}$ Calogero-Sutherland hyperbolic system, whereas the $\mathcal{N}=4$ model contains additional semi-dynamical spin variables and is an extension of the U(2) spin Calogero-Sutherland hyperbolic system. We construct two different versions of the $\mathcal{N}=4$ model, with and without the interacting center-of-mass coordinate in the bosonic sector.