Supersymmetric Calogero-Type Models via Gauging in Superspace

Abstract

A new kind of \({\mathscr {N}}=2\) and \({\mathscr {N}}=4\) supersymmetric extensions of both the rational and hyperbolic Calogero models is derived by gauging U(n) symmetry of the appropriate superfield matrix models. The common feature of these systems is the non-standard number \({\mathscr {N}}n^2\) of fermionic variables. An essential ingredient of the construction of \({\mathscr {N}}=4\) models is the semi-dynamical spin variables described by \(d=1\) Wess-Zumino terms. The bosonic cores of \({\mathscr {N}}=4\) models are U(2) spin Calogero and Calogero-Sutherland models. In the hyperbolic case there exist two non-equivalent \({\mathscr {N}}=4\) extensions, with and without the interacting center-of-mass coordinate in the bosonic sector.