Some Exact Results in QCD-like Theories

Abstract

I propose a controlled approximation to QCD-like theories with massless quarks by employing supersymmetric QCD perturbed by anomaly-mediated supersymmetry breaking. They have identical massless particle contents. Thanks to the ultraviolet-insensitivity of anomaly mediation, dynamics can be worked out exactly when $m\ll \Lambda$, where $m$ is the size of supersymmetry breaking and $\Lambda$ the dynamical scale of the gauge theory. I demonstrate that chiral symmetry is dynamically broken for $N_f\le \frac{3}{2}{N}_c$ while the theories lead to non-trivial infrared fixed points for larger number of flavors. While there may be a phase transition as $m$ is increased beyond $\Lambda$, qualitative agreements with expectations in QCD are encouraging and suggest that two limits $m\ll \Lambda$ and $m\gg \Lambda$ may be in the same universality class.

Comments: 6 pages, 2 figures. Argument strengthened with Naive Dimensional Analysis. A reference added. Several typos fixed. Version accepted for publication in Physical Review Letters