Supersymmetry breakdown for an extended version of the Nicolai supersymmetric fermion lattice model

TL;DR

This paper proves that the extended Nicolai supersymmetric fermion lattice model exhibits dynamical supersymmetry breaking for all non-zero parameter values, with positive energy density in homogeneous ground states.

Contribution

It demonstrates that the extended Nicolai model breaks supersymmetry dynamically for any non-zero parameter, extending previous studies to a broader class of models.

Findings

Supersymmetry is broken for all non-zero g.

Homogeneous ground states have strictly positive energy density.

The model extends the original Nicolai supersymmetric fermion lattice model.

Abstract

Sannomiya-Katsura-Nakayama have recently studied supersymmetry breakdown for an extension of the Nicolai supersymmetric fermion lattice model. This model called the extended Nicolai model is parameterized by an adjustable constant $g\in \mathbb{R}$ in its defining supercharge, and satisfies ${{\cal{N}}}=2$ supersymmetry. We show that for any non-zero $g$ the extended Nicolai model breaks supersymmetry dynamically, and the energy density of any homogeneous ground state (that breaks supersymmetry) is strictly positive.