SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology

Abstract

We calculate the low-lying glueball spectrum, some string tensions and some properties of topology and the running coupling for SU(N) lattice gauge theories in 3+1 dimensions. We do so for N = 2,3,...12, using lattice simulations with the Wilson plaquette action, and for glueball states in all the representations of the cubic rotation group, for both values of parity and charge conjugation. We extrapolate these results to the continuum limit of each theory and then to N=infinity. For a number of these states we are able to identify their continuum spins with very little ambiguity. We calculate the fundamental string tension and k=2 string tension and investigate the N dependence of the ratio. Using the string tension as the scale, we calculate the running of a lattice coupling and confirm that g(a)**2 varies as 1/N for constant physics as N->oo. We fit our calculated values of the string tension with the 3-loop beta-function, and extract a value for Lambda-MSbar, in units of the string tension, for all our values of N, including SU(3). We calculate the topological charge Q for N=2,..,6 where it fluctuates sufficiently for a plausible estimate of the continuum topological susceptibility. We also calculate the renormalisation of the lattice topological charge, ZQ(beta), for all our SU(N) gauge theories, using a standard definition of the charge, and we provide interpolating formulae, which may be useful in estimating the renormalisation of the lattice theta parameter. We provide quantitative results for how the topological charge `freezes' with decreasing lattice spacing and with increasing N, and show how we cicumvent this issue in our calculations.

122 pages; extended and improved text; many tables and figures of earlier version removed for brevity; as accepted for publication

References in corpus (12)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Finite volume QCD at fixed topological charge
• Glueball masses in the large N limit
• Closed flux tubes and their string description in D=3+1 SU(N) gauge theories
• Flux Tube Spectra from Approximate Integrability at Low Energies
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Universal Subleading Spectrum of Effective String Theory
• On the running of the bare coupling in SU(N) lattice gauge theories
• Glueballs and Strings in $Sp(2N)$ Yang-Mills theories
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Ergodic sampling of the topological charge using the density of states

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