Supersymmetric Calogero and Calogero-Sutherland models from gauging

Abstract

We describe how the new kinds of N = 2 and N = 4 supersymmetric extensions of the rational and hyperbolic Calogero models can be derived by gauging U(n) symmetry of the appropriate superfield matrix models. These systems feature non-standard numbers N n2 of physical fermionic variables as compared with N n in the standard case. An essential ingredient of N = 4 models is the necessary presence of semi-dynamical spin variables described by d = 1 Wess-Zumino terms. The bosonic cores of N = 4 models are U(2) spin Calogero and Calogero-Sutherland models. In the hyperbolic case two non-equivalent N = 4 extensions exist, with and without the interacting center-of-mass coordinate in the bosonic sector. The talk is based on joint works with Sergey Fedoruk and Olaf Lechtenfeld.