  Recently Appelquist, Terning, and Wijewardhana investigated the zero
temperature chiral phase transition in SU(N) gauge theory as the number of
fermions N_f is varied. They argued that there is a critical number of fermions
N^c_f, above which there is no chiral symmetry breaking and below which chiral
symmetry breaking and confinement set in. They further argued that that the
transition is not second order even though the order parameter for chiral
symmetry breaking vanishes continuously as N_f approaches N^c_f on the broken
side. In this note I propose a simple physical picture for the spectrum of
states as N_f approaches N^c_f from below (i.e. on the broken side) and argue
that this picture predicts very different and non-universal behavior than is
the case in an ordinary second order phase transition. In this way the
transition can be continuous without behaving conventionally. I further argue
that this feature results from the (presumed) existence of an infrared
Banks-Zaks fixed point of the gauge coupling in the neighborhood of the chiral
transition and therefore depends on the long-distance nature of the non-abelian
gauge force.
