Comments on Condensates in Non-Supersymmetric Orbifold Field Theories

Non-supersymmetric orbifolds of N = 1 super Yang-Mills theories are conjectured to inherit properties from their supersymmetric parent. We examine this conjecture by compactifying the Z2 orbifold theories on a spatial circle of radius R. We point out that when the orbifold theory lies in a specific weakly coupled vacuum, fractional instantons do give rise to the conjectured condensate of bi-fundamental fermions. However, we show that quantum effects render this vacuum unstable through the generation of twisted operators. In the true vacuum state, no fermion condensate forms. Thus, in contrast to super YangMills, the compactified orbifold theory undergoes a chiral phase transition as R is varied.