Solution of gauge theories induced by fundamental representation scalars

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 $\epsilon=N_c/N_f$, it undergoes a phase transition at a critical value, $\epsilon_c(D)$, for $D>2$.