SU(N) gauge theories in 2+1 dimensions -- further results

TL;DR

This paper computes the string tension and mass spectrum of SU(N) gauge theories in 2+1 dimensions for various N, providing evidence for linear confinement at large N and refining the understanding of large-N corrections.

Contribution

It extends previous lattice calculations to SU(4) and SU(6), improving the extrapolation to N=infinity and analyzing the large-N behavior of these theories.

Findings

SU(N) theories in 2+1 dimensions are linearly confining as N approaches infinity.

Leading large-N correction is proportional to 1/N^2.

No evidence found for the expected multiplication of states in flux loop models.

Abstract

We calculate the string tension and part of the mass spectrum of SU(4) and SU(6) gauge theories in 2+1 dimensions using lattice techniques. We combine these new results with older results for N=2,...,5 so as to obtain more accurate extrapolations to N=infinity. The qualitative conclusions of the earlier work are unchanged: SU(N) theories in 2+1 dimensions are linearly confining as N->infinity; the limit is achieved by keeping g.g.N fixed; SU(3), and even SU(2), are `close' to SU(infinity). We obtain more convincing evidence than before that the leading large-N correction is O(1/N.N). We look for the multiplication of states that one expects in simple flux loop models of glueballs, but find no evidence for this.