Nonlinear supersymmetry: from classical to quantum mechanics

TL;DR

This paper explores the quantization challenges of nonlinear supersymmetry, addressing quantum anomalies and proposing corrections to preserve supersymmetry at the quantum level, with insights from superconformal symmetry examples.

Contribution

It introduces methods to correct quantum anomalies in nonlinear supersymmetry, enhancing understanding of supersymmetry preservation during quantization.

Findings

Certain superpotentials admit integrals of motion with corrections

Corrections can preserve nonlinear supersymmetry at the quantum level

Analysis of superconformal symmetry illustrates correction mechanisms

Abstract

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum level. With an example of the system realizing the nonlinear superconformal symmetry, we discuss the nature of such corrections and speculate on their possible general origin.