Quantum Mechanics in Non(Anti)Commutative Superspace

TL;DR

This paper explores non(anti)commutative deformations of superspace in quantum mechanics, revealing preserved supersymmetry, a smeared superpotential, and unexpected conserved charges, thus deepening understanding of deformed supersymmetric systems.

Contribution

It introduces a novel deformed quantum mechanics framework with preserved supersymmetry and constructs a nonlinear realization of the supersymmetry algebra.

Findings

Deformation preserves half of the supercharge algebra.

Superpotential becomes smeared in the deformed theory.

A second conserved charge leads to a nonlinear supersymmetry realization.

Abstract

We consider non(anti)commutative (NAC) deformations of d=1 N=2 superspace. We find that, in the chiral base, the deformation preserves only a half of the original (linearly realized) supercharge algebra, as it usually happens in NAC field theories. We obtain in terms of a real supermultiplet a closed expression for a deformed Quantum Mechanics Lagrangian in which the original superpotential is smeared, similarly to what happens for the two dimensional deformed sigma model. Quite unexpectedly, we find that a second conserved charge can be constructed which leads to a nonlinear field realization of the supersymmetry algebra, so that finally the deformed theory has as many conserved supercharges as the undeformed one. The quantum behavior of these supercharges is analyzed.