$\mathcal{N}=2$ supersymmetry and anisotropic scale invariance

TL;DR

This paper introduces a new class of $ =2$ supersymmetric quantum systems that exhibit anisotropic scaling with distinct space and time exponents, extending previous models like the inverse square potential.

Contribution

It generalizes the known supersymmetric inverse square potential to a broader class of systems with anisotropic scale invariance and no scale anomaly.

Findings

Constructed scale-anomaly-free $ =2$ supersymmetric models

Demonstrated non-vanishing potentials with anisotropic scaling

Extended the class of supersymmetric systems beyond known cases

Abstract

We find a class of scale-anomaly-free $\mathcal{N}=2$ supersymmetric quantum systems with non-vanishing potential terms where space and time scale with distinct exponents. Our results generalise the known case of the supersymmetric inverse square potential to a larger class of scaling symmetries.