Superconformal mechanics and nonlinear supersymmetry

Abstract

We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n$, $n\in \mathbb{N}$, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum systems are characterized by the nonlinear superconformal symmetry. It is generated by the four bosonic integrals which form the so(1,2) x u(1) subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2 so(1,2)-representations and anticommuting for the order n polynomials of the even generators. We find that the modified quantum system with an integer value of the parameter $\alpha$ is described simultaneously by the two nonlinear superconformal symmetries of the orders relatively shifted in odd number. For the original quantum model with $|\alpha |=p$, $p\in \mathbb{N}$, this means the presence of the order 2p nonlinear superconformal symmetry in addition to the osp(2|2) supersymmetry.

16 pages; misprints corrected, note and ref added, to appear in JHEP

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