Euclidean lattice simulation for the dynamical supersymmetry breaking

TL;DR

This paper proposes a lattice simulation method to detect spontaneous supersymmetry breaking by measuring ground-state energy, and applies it to supersymmetric models, finding no evidence of breaking in a specific super Yang-Mills theory.

Contribution

It introduces a lattice-based approach to observe supersymmetry breaking through ground-state energy and tests it on supersymmetric models, including a two-dimensional super Yang-Mills theory.

Findings

Confirmed the method in supersymmetric quantum mechanics

Applied the method to 2D super Yang-Mills theory with SU(2)

Found no spontaneous supersymmetry breaking in the studied model

Abstract

The global supersymmetry is spontaneously broken if and only if the ground-state energy is strictly positive. We propose to use this fact to observe the spontaneous supersymmetry breaking in euclidean lattice simulations. For lattice formulations that possess a manifest fermionic symmetry, there exists a natural choice of a hamiltonian operator that is consistent with a topological property of the Witten index. We confirm validity of our idea in models of the supersymmetric quantum mechanics. We then examine a possibility of a dynamical supersymmetry breaking in the two-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory with the gauge group $\SU(2)$, for which the Witten index is unknown. Differently from a recent conjectural claim, our numerical result tempts us to conclude that supersymmetry is not spontaneously broken in this system.