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.