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

TL;DR

This paper investigates SU(N) gauge theories in 3+1 dimensions by calculating glueball spectra, string tensions, and topological properties across N=2 to 12, extrapolating to the continuum and large N limits, and analyzing the running coupling and topological susceptibility.

Contribution

It provides comprehensive lattice simulation results for SU(N) gauge theories, including continuum extrapolations, N-infinity limits, and detailed topological and string tension analyses, with new insights into the N dependence of these quantities.

Findings

Glueball spectra identified with continuum spins.

String tension ratios and N dependence analyzed.

Topological susceptibility estimated for N=2 to 6.

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.