Exact solution of d=1 Kazakov-Migdal induced gauge theory

TL;DR

This paper provides an exact solution for the D=1 Kazakov-Migdal induced gauge theory on a compactified lattice, revealing connections to the vortex-free sector of D=1 bosonic string theory and matching previous continuum results.

Contribution

It presents the first exact solution of the D=1 Kazakov-Migdal model for arbitrary sites and N, linking it to string theory sectors and continuum limits.

Findings

Partition function explicitly derived for D=1 model

Connection established with vortex-free sector of bosonic string

Results match previous continuum limit analyses

Abstract

We give the exact solution of the Kazakov-Migdal induced gauge model in the case of a D=1 compactified lattice with a generic number $S$ of sites and for any value of N. Due to the peculiar features of the model, the partition function that we obtain also describes the vortex-free sector of the D=1 compactified bosonic string, and it coincides in the continuum limit with the one obtained by Boulatov and Kazakov in this context.