SO(2N) and SU(N) gauge theories in 2+1 dimensions

TL;DR

This paper investigates how SO(2N) gauge theories in 2+1 dimensions approach their large-N limit and compares their spectra and mass ratios to SU(N) theories, highlighting similarities and differences.

Contribution

It provides the first detailed numerical comparison of SO(2N) and SU(N) gauge theories in 2+1 dimensions, confirming spectral similarities and elucidating differences in string tension and coupling.

Findings

SO(6) and SU(4) spectra are similar

Mass ratios agree in the large-N limit

Differences in string tension and coupling explained

Abstract

We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N=oo limit. This question has recently become topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge theories, but do not have a finite chemical potential sign problem. We consider only the pure gauge theory and, because of the inconvenient location of the lattice strong-to-weak coupling 'bulk' transition in 3+1 dimensions, we largely confine our numerical calculations to 2+1 dimensions. We discuss analytic expectations in both D=2+1 and D=3+1, show that the SO(6) and SU(4) spectra do indeed appear to be the same, and show that a number of mass ratios do indeed appear to agree in the large-N limit. In particular SO(6) and SU(3) gauge theories are quite similar except for the values of the string tension and coupling, both of which differences can be readily understood.