The deconfining phase transition of SO(N) gauge theories in 2+1 dimensions
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 ∈ [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.
On the weak N-dependence of SO(N) and SU(N) gauge theories in 2 + 1 dimensions
Abstract:
We consider (continuum) mass ratios of the lightest ‘glueballs’ as a function of N for SO(N) and SU(N) lattice gauge theories in D = 2 + 1. We observe that the leading large N correction is usually sufficient to describe the N-dependence of SO(N ≥ 3) and SU(N ≥ 2), within the errors of the numerical calculation. Just as interesting is the fact that the coefficient of this correction almost invariably turns out to be anomalously small, for both SO(N) and SU(N). We point out that this can follow naturally from the strong constraints that one naively expects from the Lie algebra equivalence between certain SO(N) and SU(N') theories and the equivalence of SO(∞) and SU(∞). The same argument for a weak N-dependence can in principle apply to SU(N) and SO(N) gauge theories in D = 3 + 1.