Comments on Condensates in Non-Supersymmetric Orbifold Field Theories

TL;DR

This paper investigates whether non-supersymmetric orbifold theories inherit properties from supersymmetric parent theories, finding that quantum effects prevent condensate formation in the true vacuum, leading to a chiral phase transition.

Contribution

It provides a detailed analysis of condensate formation and vacuum stability in non-supersymmetric orbifold theories upon compactification, challenging previous conjectures.

Findings

Fractional instantons produce condensates in weakly coupled vacua.

Quantum effects destabilize the vacuum, preventing condensate formation.

A chiral phase transition occurs as the compactification radius varies.

Abstract

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 Z_2 orbifold theories on a spatial circle of radius R. We point out that when the orbifold theory lies in the weakly coupled vacuum of its parent, fractional instantons do give rise to the conjectured condensate of bi-fundamental fermions. Unfortunately, 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 Yang-Mills, the compactified orbifold theory undergoes a chiral phase transition as R is varied.