Superconformal Calogero models as a gauged matrix mechanics

TL;DR

This paper develops a gauged superfield approach to construct N-superconformal multi-particle Calogero models, illustrating it with systems exhibiting SU(1,1|1) and D(2,1;α) supersymmetries and a new N=4 superconformal quantum mechanics.

Contribution

It introduces a novel gauged superfield method for building N-superconformal Calogero models, expanding the toolkit for supersymmetric multi-particle systems.

Findings

Constructed multi-particle systems with SU(1,1|1) and D(2,1;α) supersymmetries

Developed a new N=4 superconformal quantum mechanics model

Demonstrated the effectiveness of the gauged superfield approach

Abstract

We present basics of the gauged superfield approach to constructing N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by the multi-particle systems possessing SU(1,1|1) and D(2,1;\alpha) supersymmetries, as well as by the model of new N=4 superconformal quantum mechanics.