Superconformal mechanics and nonlinear supersymmetry

TL;DR

This paper demonstrates that changing the coupling constant in superconformal mechanics induces a shift from linear to nonlinear superconformal symmetry, revealing new algebraic structures and dual symmetries in the quantum system.

Contribution

It introduces a novel class of nonlinear superconformal symmetries arising from a simple coupling constant modification in superconformal mechanics models.

Findings

Modified systems exhibit nonlinear superconformal symmetry.

Quantum systems with integer alpha have dual nonlinear symmetries.

Original models show additional order 2p nonlinear superconformal symmetry.

Abstract

We show that a simple change of the classical boson-fermion coupling constant, $2\alpha \to 2\alpha n $, $n\in \N$, 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 $|\alpha|=p$, $p\in \N$, this means the presence of the order 2p nonlinear superconformal symmetry in addition to the osp(2|2) supersymmetry.