Conformal and Superconformal Mechanics

TL;DR

This paper explores the conditions under which non-relativistic spinning particles in curved backgrounds with magnetic fields exhibit conformal and superconformal symmetry, revealing geometric links and presenting new models.

Contribution

It derives necessary conditions for conformal and superconformal invariance in such systems and introduces new examples demonstrating these symmetries.

Findings

Identified geometric conditions for conformal invariance

Derived constraints on couplings for superconformal symmetry

Presented new models with conformal and superconformal properties

Abstract

We investigate the conformal and superconformal properties of a non-relativistic spinning particle propagating in a curved background coupled to a magnetic field and with a scalar potential. We derive the conditions on the couplings for a large class of such systems which are necessary in order their actions admit conformal and superconformal symmetry. We find that some of these conditions can be encoded in the conformal and holomorphic geometry of the background. Several new examples of conformal and superconformal models are also given.