Normalization of the Ground State of the Supersymmetric Harmonic Oscillator

TL;DR

This paper investigates the normalization of the ground state in the supersymmetric harmonic oscillator, highlighting the limitations of perturbation theory in explaining supersymmetry breaking.

Contribution

It provides a detailed analysis showing perturbation theory's failure to correctly normalize the ground state and explain supersymmetry breaking in the supersymmetric harmonic oscillator.

Findings

Perturbation theory yields incorrect ground-state wave function

Perturbation theory fails to explain supersymmetry breaking

Normalization issues are critical in supersymmetric models

Abstract

Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken. Supersymmetry may be broken spontaneously at any order of perturbation theory or dynamically due to nonperturbative effects. To examine the methods of supersymmetry breaking, special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. This study explains that perturbation theory gives incorrect results for both the ground-state wave function and the energy spectrum and it fails to give an explanation to the supersymmetry breaking.