Extended supersymmetry and its reduction on a circle with point singularities

TL;DR

This paper explores extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities, constructing supercharges, analyzing compatible singularities, and studying spectrum degeneracy and supersymmetry breaking.

Contribution

It explicitly constructs odd-numbered supercharges using discrete transformations and clarifies the class of singularities compatible with supersymmetry, including reductions to lower supersymmetry.

Findings

Constructed N=2n+1 supercharges explicitly.

Identified singularities compatible with supersymmetry.

Analyzed spectrum degeneracy and spontaneous supersymmetry breaking.

Abstract

We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of singularities compatible with supersymmetry is clarified. In our formulation, the supersymmetry can be reduced to $M$-extended supersymmetry for any integer $M<N$. The degeneracy of the spectrum and spontaneous supersymmetry breaking are also studied.