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 ∈ [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 =∞ 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) × SU(2), motivated by the fact that these pairs of gauge theories share the same Lie algebras.