Observing dynamical supersymmetry breaking with euclidean lattice simulations

TL;DR

This paper proposes a method to observe dynamical supersymmetry breaking using Euclidean lattice simulations by measuring the ground-state energy through the Hamiltonian expectation value with antiperiodic boundary conditions, and confirms its validity in supersymmetric quantum mechanics models.

Contribution

It introduces a novel approach to detect supersymmetry breaking on the lattice by leveraging the ground-state energy and tests this in supersymmetric models, challenging previous conjectures.

Findings

Confirmed the method in supersymmetric quantum mechanics

Applied the approach to 2D super Yang-Mills theory

Did not observe positive ground-state energy within errors

Abstract

A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an \emph{antiperiodic} temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of 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. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.