Abstract:We calculate the spectrum of light glueballs and the string tension in a number of SO(N ) lattice gauge theories in 2+1 dimensions, with N in the range 3 ≤ N ≤ 16. After extrapolating to the continuum limit and then to N = ∞ we compare to the spectrum and string tension of the SU(N → ∞) gauge theory and find that the most reliably and precisely calculated physical quantities are consistent in that limit. We also compare the glueball spectra of those pairs of SO(N ) and SU(N ) theories that possess the same Lie algebra, i.e. SO(3) and SU(2), SO(4) and SU(2)×SU(2), SO(6) and SU(4), and find that for the very lightest glueballs the spectra are consistent within each such pair, as are the string tensions and the couplings. Where there are apparent discrepancies they are typically for heavier glueballs, where the systematic errors are much harder to control. We calculate the SO(N ) string tensions with a particular focus on the confining properties of SO(2N + 1) theories which, unlike SO(2N ) theories, possess a trivial centre. We find that for both the light glueballs and for the string tension SO(2N ) and SO(2N + 1) gauge theories appear to form a single smooth sequence.
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.
We perform an exploratory investigation of how rapidly the physics of SO(2N) gauge theories approaches its N = ∞ limit. This question has recently become topical because SO(2N) gauge theories are orbifold equivalent to SU(N) gauge theories, but do not have a finite chemical potential sign problem. We consider only the pure gauge theory and, because of the inconvenient location of the lattice strong-to-weak coupling 'bulk' transition in 3+1 dimensions, we largely confine our numerical calculations to 2+1 dimensions. We discuss analytic expectations in both D = 2 + 1 and D = 3 + 1, show that the SO(6) and SU(4) spectra do indeed appear to be the same, and show that a number of mass ratios do indeed appear to agree in the large-N limit. In particular SO(6) and SU(3) gauge theories are quite similar except for the values of the string tension and coupling, both of which differences can be readily understood.
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