Natural Breaking of Supersymmetry

TL;DR

This paper investigates how supersymmetry can be broken naturally by analyzing Green's functions and Schwinger-Dyson equations in the Wess-Zumino model, revealing deviations from non-renormalization and Ward identities, and showing enhanced mass splitting.

Contribution

It demonstrates the explicit breakdown of supersymmetry in the Wess-Zumino model beyond perturbation theory through non-perturbative solutions of Schwinger-Dyson equations.

Findings

Deviation from non-renormalization theorem in perturbation theory

Ward identities are violated in the analyzed formalism

Mass splitting between fermions and bosons is increased beyond perturbative estimates

Abstract

The loop structure of two point Green's functions is investigated in the Wess-Zumino model in the formalism where the auxiliary fields are integrated out. In the usual frame of perturbation theory the deviation from the non-renormalization theorem is explicitly shown. It is shown that Ward identity are not satisfied in this approach. Further we go beyond perturbation theory by solving a system of regularized Schwinger-Dyson equations (SDEs). The mass splitting between fermions and bosons, which was already observed in perturbation theory level, is further enhanced.