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

TL;DR

This paper provides an exact solution for a lattice gauge theory model induced by heavy scalar fields at infinite N, deriving the eigenvalue density behavior in the continuum limit across arbitrary dimensions.

Contribution

It presents the first exact solution of the induced lattice gauge theory at large N for any dimension, including the derivation of the eigenvalue density equation.

Findings

Eigenvalue density grows as a power law in the continuum limit

Derived nonlinear integral equation for eigenvalue density

Solution applicable for arbitrary dimension D

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 $ \phi^{\alpha} $ where $ \alpha = 1 + \frac{1}{\pi}\arccos\frac{D}{3D-2} $.