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.
Highlights
While a great deal is known about the non-perturbative physics of SU(N ) gauge theories from calculations on the lattice, much less is known about SO(N ) gauge theories
While we shall provide some evidence for confinement at low T in this paper, the explicit evidence for the confinement being linear is given in our companion paper on the glueball spectra and string tensions [12], where we show that the energy of closed flux tubes is proportional to their length for both odd and even N
In this paper we identified a finite temperature transition in D = 2 + 1 SO(N ) gauge theories for N = 4, 5, 6, 7, 8, 9, 12, 16
Summary
While a great deal is known about the non-perturbative physics of SU(N ) gauge theories from calculations on the lattice, much less is known about SO(N ) gauge theories. To the extent that the difference in the global properties of the groups (such as the centre) is not important, we would expect the deconfining transition and temperature to be identical within each of these pairs of gauge theories, and this is something we shall attempt to check. Assuming this identity, the known value of Tc in SU(2) provides us with a value for SO(3), which we do not calculate directly (for reasons given below). In addition all these calculations will allow us to compare SO(2N ) and SO(2N + 1) theories, which is interesting because SO(2N + 1) gauge theories have a trivial center in contrast to the non-trivial Z2 center of SO(2N ) theories
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