Solution of gauge theories induced by fundamental representation scalars

Abstract

Gauge theories induced by scalars in the fundamental representation of the $U(N_c{)}_{gauge}\times U(N_f{)}_{global}$ group are investigated in the large $N_c$ and $N_f$ limit. A master field is defined from bilinears of the scalar field following an Eguchi-Kawai type reduction of spacetime. The density function for the master field satisfies an integral equation that can be solved exactly in two dimensions (D=2) and in a convergent series of approximations at $D>2$. While at D=2 the system is in the same phase at all $ϵ=N_c/N_f$, it undergoes a phase transition at a critical value, ${ϵ}_c(D)$, for $D>2$.

Comments: 12 pages, LaTeX