Instantons and the Chiral Phase Transition

Abstract

We examine the role of instantons in the zero-temperature chiral phase transition in an SU(N) gauge theory. For a range of N_f (the number of fermion flavors) depending on N, the theory exhibits an infrared fixed point at coupling ${\alpha }_{\ast }$. As N_f decreases, ${\alpha }_{\ast }$ increases, and it eventually exceeds a critical value sufficient to trigger chiral symmetry breaking. For the case N = 2, we estimate the critical values of N_f and ${\alpha }_{\ast }$ due to instantons by numerically solving a gap equation with an instanton-generated kernel. We find instanton effects of strength comparable to that of gluon exchange.

Comments: LaTeX, 9 pages, including 2 figures in EPS format