  We propose and study at large N a new lattice gauge model , in which the
Yang-Mills interaction is induced by the heavy scalar field in adjoint
representation. At any dimension of space and any $ N $ the gauge fields can be
integrated out yielding an effective field theory for the gauge invariant
scalar field, corresponding to eigenvalues of the initial matrix field. This
field develops the vacuum average, the fluctuations of which describe the
elementary excitations of our gauge theory. At $N= \infty $ we find two phases
of the model, with asymptotic freedom corresponding to the strong coupling
phase (if there are no phase transitions at some critical $N$). We could not
solve the model in this phase, but in the weak coupling phase we have derived
exact nonlinear integral equations for the vacuum average and for the scalar
excitation spectrum. Presumably the strong coupling equations can be derived by
the same method.
