New many-body superconformal models as reductions of simple composite systems

We propose a new reduction mechanism which allows one to construct n-particle (super)conformal theories with a pairwise interaction starting from a composite system involving n(n- 1)/2+ 1 copies of the ordinary (super)conformal mechanics. Applications of the scheme include an N=4 superconformal extension for a complexification of the Calogero model and a D(2,1|α)-invariant n-particle system.