Exact Solution of Induced Lattice Gauge Theory at Large $N$

Abstract

We find the exact solution of a recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation at $N=\infty$ for arbitrary dimension $D$. The nonlinear integral equation for the gauge invariant density of eigenvalues of the vacuum average of the scalar field is derived. In the continuum limit, the density grows as ${\varphi }^{\alpha }$ where $\alpha =1+\frac{1}{\pi }\arccos \frac{D}{3D-2}$.

PUPT-1323