Supersymmetric hyperbolic Calogero-Sutherland models by gauging

Abstract

Novel $\mathcal{N}=2$ and $\mathcal{N}=4$ supersymmetric extensions of the Calogero-Sutherland hyperbolic systems are obtained by gauging the $\mathrm{U}(n)$ isometry of matrix superfield models. The bosonic core of the $\mathcal{N}=2$ models is the standard $A_{n-1}$ 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.

1+18 pages; v2: one reference added, minor corrections, matches published version

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