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
×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
.