SU(N)gauge theories in 2+1 dimensions

Abstract

We calculate the mass spectra and string tensions of SU(2), SU(3), SU(4) and SU(5) gauge theories in 2+1 dimensions. We do so by simulating the corresponding lattice theories and then extrapolating dimensionless mass ratios to the continuum limit. We find that such mass ratios are, to a first approximation, independent of the number of colours, N c , and that the remaining dependence can be accurately reproduced by a simple O(1/N 2 c ) correction. This provides us with a prediction of these mass ratios for all SU(N c ) theories in 2+1 dimensions and demonstrates that these theories are already 'close' to N c = ∞ for N c ≥ 2. We find that the theory retains a non-zero confining string tension as N c → ∞ and that the dimensionful coupling g 2 is proportional to 1/N c at large N c , when expressed in units of the dynamical length scale of the theory. During the course of these calculations we study in detail the effects of including over-relaxation in the Monte Carlo, of using a mean-field improved coupling to extrapolate to the continuum limit, and the use of space-time asymmetric lattice actions to resolve heavy glueball correlators. ×

Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

“…These expectations are largely based on an analysis of all-orders perturbation theory, so it is interesting to ask how precisely they are confirmed by non-perturbative lattice calculations. This question has been addressed in the past [53,59,60], but here we can go somewhat further using the very precise string tensions calculated for N ∈ [2,8] in [22]. We display in figure 1 the continuum values of √ σ/g 2 N taken from the first row of table 2 in [22].…”

“…we will obtain them as am i (a). To obtain the continuum limit one can take ratios of masses, calculate these over some substantial range of a, and extrapolate to a = 0, using the leading correction that is known to be O(a 2 ) for our plaquette action: [53] that the approach to the continuum limit for typical dynamical quantities is very rapid. An alternative approach is to calculate the continuum value of m i /g 2 , using eq.…”

“…The lattice correction is O(1/β) ∝ O(a) rather than O(a 2 ) because different lattice coupling definitions will clearly differ at this order. In this way one can, for example, calculate the continuum string tension in units of g 2 [22,53].…”

Static potential and local color fields in unquenched three-dimensional lattice QCD

“…QCD 3 has been shown to share most of the fundamental properties of the realistic 4-d QCD [5] and thus provides excellent insights to QCD. The coupling g 2 0 in QCD 3 has dimension of mass and so explicitly sets the mass scale for the theory, i.e., m ∝ g 2 0 for any mass quantity m. In order to have some intuition for this mass scale, we express this scale in terms of the length scale in 4-d -"fermi" (f m).…”

“…The coupling g 2 0 in QCD 3 has dimension of mass and so explicitly sets the mass scale for the theory, i.e., m ∝ g 2 0 for any mass quantity m. In order to have some intuition for this mass scale, we express this scale in terms of the length scale in 4-d -"fermi" (f m). Motivated by the fact that both 3-d and 4-d QCD are linearly confining, we match the quenched continuum extrapolation of the 3-d string tension, √ σ/g 2 = 0.3353(18) [5], with …”