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

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 is an element of [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) x SU(2), motivated by the fact that these pairs of gauge theories share the same Lie algebras.