# SO(N) gauge theories in 2+1 dimensions: glueball spectra and confinement

## TL;DR

This paper computes the glueball spectra and string tensions of SO(N) gauge theories in 2+1 dimensions for N=3 to 16, compares them with SU(N) theories, and investigates their confining properties and continuum limits.

## Contribution

It provides the first detailed comparison of SO(N) and SU(N) gauge theories in 2+1 dimensions, including continuum extrapolations and analysis of theories with trivial centers.

## Key findings

- Spectra and string tensions are consistent between SO(N) and SU(N) in the large N limit.
- Light glueball spectra are similar for SO(N) and SU(N) theories with the same Lie algebra.
- SO(2N) and SO(2N+1) theories form a smooth sequence in physical properties.

## Abstract

We calculate the spectrum of light glueballs and the string tension in a number of SO(N) lattice gauge theories in 2+1 dimensions, with N in the range from N=3 to N=16. After extrapolating to the continuum limit and then to N=oo we compare to the spectrum and string tension of the SU(N=oo) gauge theory and find that the most reliably and precisely calculated physical quantities are consistent in that limit. We also compare the glueball spectra of those pairs of SO(N) and SU(N') theories that possess the same Lie algebra, i.e. SO(3) and SU(2), SO(4) and SU(2)xSU(2), SO(6) and SU(4), and find that for the very lightest glueballs the spectra are consistent within each such pair, as are the string tensions and the couplings. Where there are apparent discrepancies they are typically for heavier glueballs, where the systematic errors are much harder to control. We calculate the SO(N) string tensions with a particular focus on the confining properties of SO(2N+1) theories which, unlike SO(2N) theories, possess a trivial centre. We find that for both the light glueballs and for the string tension SO(2N) and SO(2N+1) gauge theories appear to form a single smooth sequence.