On Methods for Extracting Exact Non-perturbative Results in Non-supersymmetric Gauge Theories

Abstract

At large N, a field theory and its orbifolds (given by projecting out some of its fields) share the same planar graphs. If the parent-orbifold relation continues even nonperturbatively, then properties such as confinement and chiral symmetry breaking will appear in both parent and orbifold. N=1 supersymmetric Yang-Mills has many nonsupersymmetric orbifolds which resemble QCD. A nonperturbative parent-orbifold relation predicts many surprising effects, exactly valid at large N, and expected to suffer only mild 1/N corrections. These include degeneracies among bosonic hadrons and exact predictions for domain wall tensions. Other predictions are valid even when supersymmetry in the parent is broken. Since these theories are QCD-like, simulation is possible, so these predictions may be numerically tested. The method also relates wide classes of nonsupersymmetric theories.

Figures (1)

• Figure 1: ${\cal N}=1$ supersymmetric Yang-Mills and its ${\bf Z}_2$, ${\bf Z}_3$ and ${\bf Z}_4$ orbifolds.