The Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories

We investigate the zero temperature chiral phase transition in an SU(N) gauge theory as the number of fermions Nf is varied. We argue that there exists a critical number of fermions N cf, above which there is no chiral symme-try breaking or confinement, and below which both chiral symmetry breaking and confinement set in. We estimate N cf and discuss the nature of the phase transition. An SU(N) gauge theory, even at zero temperature, can exist in different phases depending on the number of massless fermions Nf in the theory. The phases are defined by whether or not chiral symmetry breaking takes place. For QCD with two or three light quarks, chiral symmetry breaking and confinement occur at roughly the same scale. By contrast, in any SU(N) gauge theory, asymptotic freedom (and hence chiral symmetry breaking and confinement) is lost if the number of fermions is larger than a certain value ( = 11N/2 for fermions in the fundamental representation)