Kazakov-Migdal Induced Gauge Theory and the Coupling of 2D Quantum Gravity to D=1 Matter

TL;DR

This paper reviews the exact solution of the Kazakov-Migdal model in one dimension, exploring its connection to 2D quantum gravity coupled to matter and presenting new results on model modifications.

Contribution

It provides an exact solution for the 1D Kazakov-Migdal model and investigates its relation to 2D quantum gravity and string theory, including new model extensions.

Findings

Exact solution of the 1D Kazakov-Migdal model

Connection to vortex-free sector of 1D bosonic string

New results on linear term addition and SU(N) restriction

Abstract

Recently Kazakov and Migdal proposed a new approach to the large $N$ limit of SU(N) gauge theories which could hopefully describe the asymptotically free fixed point of QCD in 4 dimensions. In this contribution we review the exact solution of their model in the case of a $d=1$ compactified lattice and its connection with the partition function of the vortex-free sector of the d=1 compactified bosonic string. Some new results on the addition of a linear term in the K-M model and on the SU(N) restriction of the general U(N) model are also presented.