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Solution of gauge theories induced by fundamental representation scalars
Gauge theories induced by scalars in the fundamental representation of the
group are investigated in the large
and 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
. While at D=2 the system is in the same phase at all ,
it undergoes a phase transition at a critical value, , for
.Comment: 12 pages, LaTe