Quantization Ambiguity and Supersymmetric Ground State Wave Functions

TL;DR

This paper investigates how quantization on a space with nontrivial topology, like a circle, introduces ambiguity that can break supersymmetry, revealing a novel mechanism independent of the superpotential's leading term.

Contribution

It demonstrates that supersymmetry breaking arises from quantization ambiguity related to topology, not just boundary conditions or superpotential form.

Findings

Supersymmetry can be broken by an undetermined parameter interpreted as a gauge field.

Breaking mechanism is similar to boundary condition effects in quantum field theory.

Supersymmetric harmonic oscillator emerges in the large radius limit of the model.

Abstract

Supersymmetric ground state wave functions of a model of supersymmetric quantum mechanics on $S^1$ (supersymmetric simple pendulum) are studied. Supersymmetry can be broken due to the existence of an undetermined parameter, which is interpreted as a gauge field and appears as a firm consequence of quantization on a space with a nontrivial topology such as $S^1$. The breaking does not depend on the leading term of the superpotential, contrary to the usual case. The mechanism of supersymmetry breaking is similar to that through boundary conditions of fields in supersymmetric quantum field theory on compactified space. The supersymmetric harmonic oscillator is realized in the limit of the infinite radius of $S^1$ with the strength of the oscillator being constant.