  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
$D>2$.
