Supersymmetry and discrete transformations on S^1 with point singularities

TL;DR

This paper explores N-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities, constructing supercharges and analyzing the impact of discrete transformations on the system's spectrum and supersymmetry breaking.

Contribution

It explicitly constructs N=2n supercharges for systems with point singularities and clarifies the class of singularities compatible with supersymmetry, introducing discrete transformations forming su(2) algebras.

Findings

Constructed N=2n supercharges explicitly.

Identified point singularities compatible with supersymmetry.

Discussed spectrum degeneracy and conditions for supersymmetry breaking.

Abstract

We investigate N-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer n, N=2n supercharges are explicitly constructed and a class of point singularities compatible with supersymmetry is clarified. Key ingredients in our construction are n sets of discrete transformations, each of which forms an su(2) algebra of spin 1/2. The degeneracy of the spectrum and spontaneous supersymmetry breaking are briefly discussed.