Interaction via reduction and nonlinear superconformal symmetry

Abstract

We show that the reduction of a planar free spin-1/2 particle system by the constraint fixing its total angular momentum produces the one-dimensional Akulov-Pashnev-Fubini-Rabinovici superconformal mechanics model with the nontrivially coupled boson and fermion degrees of freedom. The modification of the constraint by including the particle's spin with the relative weight $n\in \N$, $n>1$, and subsequent application of the Dirac reduction procedure (`first quantize and then reduce') give rise to the anomaly free quantum system with the order $n$ nonlinear superconformal symmetry constructed recently in hep-th/0304257. We establish the origin of the quantum corrections to the integrals of motion generating the nonlinear superconformal algebra, and fix completely its form.