Nonperturbative study of dynamical SUSY breaking in $\mathcal{N} = (2, 2)$ Yang-Mills

TL;DR

This study investigates whether supersymmetry is spontaneously broken in two-dimensional $ abla$= (2, 2) supersymmetric Yang-Mills theory by lattice simulations, finding no evidence of breaking as the ground state energy remains zero.

Contribution

The paper provides a nonperturbative lattice analysis of dynamical supersymmetry breaking in $ abla$= (2, 2) SYM, including continuum and zero-temperature extrapolations.

Findings

Ground state energy density is consistent with zero.

No evidence of dynamical supersymmetry breaking.

Simulations performed on lattices up to $96 imes 96$.

Abstract

We examine the possibility of dynamical supersymmetry breaking in two-dimensional $\mathcal{N} = (2, 2)$ supersymmetric Yang-Mills theory. The theory is discretized on a Euclidean spacetime lattice using a supersymmetric lattice action. We compute the vacuum energy of the theory at finite temperature and take the zero temperature limit. Supersymmetry will be spontaneously broken in this theory if the measured ground state energy is non-zero. By performing simulations on a range of lattices up to $96 \times 96$ we are able to perform a careful extrapolation to the continuum limit for a wide range of temperatures. Subsequent extrapolations to the zero temperature limit yield an upper bound on the ground state energy density. We find the energy density to be statistically consistent with zero in agreement with the absence of dynamical supersymmetry breaking in this theory.