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Comments on Condensates in Non-Supersymmetric Orbifold Field Theories

David Tong

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.

Comments on Condensates in Non-Supersymmetric Orbifold Field Theories

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.

Paper Structure

This paper contains 6 sections, 13 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Effective Potential and Vacuum Physics
  3. Fractional Instantons on ${\bf R}^3\times {\bf S}^1$ and the Condensate
  4. Summary
  5. Acknowledgments

Figures (1)

  • Figure 1: Three classical vacua of the theory. The solid (red) lines depict the ${\bf S}^1$ valued eigenvalues of the Wilson line for the $U(N)_1$ gauge group, while the dotted (green) lines depict the eigenvalues for $U(N)_2$. Calorons are shown as (blue) arcs connecting the eigenvalues of a given gauge group. This graphical representation finds life in the T-dual brane picture.