ZERO-TEMPERATURE CHIRAL PHASE-TRANSITION IN SU(N) GAUGE-THEORIES

Recently Appelquist, Terning, and Wijevsardhana investigated the zero- temperature chiral phase transition in SU(N) gauge theory as the numbe r of fermions N-f is varied. They argued that there is a critical numb er of fermions N-f(c), above which there is no chiral symmetry breakin g and below which chiral symmetry breaking and confinement set in. The y further argued that the transition is not second order even though t he order parameter for chiral symmetry breaking vanishes continuously as N-f approaches N-f(c) on the broken side. In this note I propose a simple physical picture for the spectrum of states as N-f approaches N -f(c) from below (i.e., on the broken side) and argue that this pictur e predicts very different and nonuniversal behavior than is the case i n an ordinary second order phase transition. In this way the transitio n can be continuous without behaving conventionally. I further argue t hat this feature results from the (presumed) existence of an infrared Banks-Zaks fixed point of the gauge coupling in the neighborhood of th e chiral transition and, therefore, depends on the long-distance natur e of the non-Abelian gauge force.