Isolated vacua in supersymmetric Yang-Mills theories

Abstract

An explicit proof of the existence of nontrivial vacua in the pure supersymmetric Yang-Mills theories with a higher orthogonal $\mathrm{SO}(N),$ $N>~7$ or the ${G}_{2}$ gauge group defined on a 3-torus with periodic boundary conditions is given. Extra vacuum states are separated by an energy barrier from the perturbative vacuum ${A}_{i}=0$ and its gauge copies.