The deconfining phase transition of SO(N) gauge theories in 2+1 dimensions

TL;DR

This study computes the deconfining temperatures of SO(N) gauge theories in 2+1 dimensions, analyzing their phase transition order and behavior as N varies, and compares them with SU(N) theories, revealing a universal N-dependent trend.

Contribution

It provides the first detailed lattice calculation of deconfining temperatures for SO(N) gauge theories in 2+1 dimensions, including their N-infinity behavior and comparison with SU(N) theories.

Findings

Deconfining temperatures of SO(N) gauge theories follow a smooth N-dependent function.

SO(N) and SU(N) deconfining temperatures agree at N=infinity.

The phase transition order varies with N, with insights into the role of the gauge group's center.

Abstract

We calculate the deconfining temperature of SO(N) gauge theories in 2+1 dimensions, and determine the order of the phase transition as a function of N, for various values of N in the range [4,16]. We do so by extrapolating our lattice results to the infinite volume limit, and then to the continuum limit, for each value of N. We then extrapolate to the N=infinity limit and observe that the SO(N) and SU(N) deconfining temperatures agree in that limit. We find that the the deconfining temperatures of all the SO(N) gauge theories appear to follow a single smooth function of N, despite the lack of a non-trivial centre for odd N. We also compare the deconfining temperatures of SO(6) with SU(4), and of SO(4) with SU(2)xSU(2), motivated by the fact that these pairs of gauge theories share the same Lie algebras.