Recently Appelquist, Terning, and Wijewardhana investigated the zero-temperature chiral phase transition in $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ gauge theory as the number of fermions $N_f$ is varied. They argued that there is a critical number of fermions $N_f^c$, above which there is no chiral symmetry breaking and below which chiral symmetry breaking and confinement set in. They further argued that the transition is not second order even though the 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 picture predicts very different and nonuniversal 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.

• Received 6 December 1996

DOI:https://doi.org/10.1103/PhysRevD.55.5238