A Study of U(N) Lattice Gauge Theory in 2-dimensions

TL;DR

This paper analyzes the U(N) lattice gauge theory in two dimensions by mapping it to a Coulomb gas model, examining its large N limit, phase transitions, and differences between finite and infinite N behaviors.

Contribution

It provides a detailed comparison of finite N and large N behaviors in 2D U(N) lattice gauge theory, highlighting the phase transition peculiarities at infinite N.

Findings

Large N limit matches finite N results near fixed points

Continuous phase transition appears only at infinite N in intermediate coupling

The infinite N phase transition is a pathology not relevant to the continuum limit

Abstract

This is an edited version of an unpublished 1979 EFI (U. Chicago) preprint: "The U(N) lattice gauge theory in 2-dimensions can be considered as the statistical mechanics of a Coulomb gas on a circle in a constant electric field. The large N limit of this system is discussed and compared with exact answers for finite N. Near the fixed points of the renormalization group and especially in the critical region where one can define a continuum theory, computations in the thermodynamic limit $(N \rightarrow \infty)$ are in remarkable agreement with those for finite and small N. However, in the intermediate coupling region the thermodynamic computation, unlike the one for finite N, shows a continuous phase transition. This transition seems to be a pathology of the infinite N limit and in this simple model has no bearing on the physical continuum limit."