SO(2N) and SU(N) gauge theories in 2 + 1 dimensions

Abstract

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.

SO(N) gauge theories in 2 + 1 dimensions: glueball spectra and confinement

“…In addition the question of whether the Z N centre symmetry, or at least its manifestation in k-strings, is recovered in some sense as one approaches N = ∞ will be addressed elsewhere. Finally we remark that our initial exploratory calculations comparing SO(N ) and SU(N ) gauge theories were presented some time ago in [15], and some of the results of the present paper have appeared in [19].…”

“…For SO(N ) lattice gauge theories the situation is different. In D = 3 + 1 one finds that the transition is again first order, but now for all N ≥ 3 [15]. Moreover at low N the value of a on the weak coupling side is very small and can pose an obstacle to accessing the continuum limit [15].…”

“…In D = 3 + 1 one finds that the transition is again first order, but now for all N ≥ 3 [15]. Moreover at low N the value of a on the weak coupling side is very small and can pose an obstacle to accessing the continuum limit [15]. (Indeed, in the case of SO(3) this has been known for a long time; for a recent discussion see [52].)…”

“…We update the fields using a natural extension to SO(N ) [15,19] of the standard SU(N ) Cabibbo-Marinari algorithm. Suppose we generate N z field configurations, {U l } I=1,...,N Z , with the measure DU exp{−S[U ]}.…”

“…The D = 3 + 1 case is clearly of more direct physical interest, but standard lattice calculations encounter an obstacle in the existence of a first-order strong to weak coupling phase transition that, for small N , occurs at a small value of the lattice spacing [15]. This means that a lattice on the weak coupling side will need to be very large in lattice units if it is to have an adequately large physical volume.…”