Physics from the lattice: glueballs in QCD; topology; SU(N) for all N

TL;DR

This work demonstrates how lattice gauge theory connects to continuum QCD through three pillars: the glueball spectrum in pure $SU(3)$, topological fluctuations and the $\eta^{\prime}$ mass via the Witten-Veneziano mechanism, and the behavior of $SU(N_c)$ gauge theories across different numbers of colors. It reviews lattice methodologies for extracting continuum glueball masses, the role of quenching, and the significance of mixing with quarkonia for interpreting experimental scalar states; it also analyzes topological charge, cooling, and the large-$N_c$ limit, presenting non-perturbative evidence that $g^2$ scales as $1/N_c$ and that spectra approach an $N_c \to \infty$ limit with small $1/N_c^2$ corrections. The results support a coherent picture in which glueballs appear as predominantly gluonic states with limited mixing, topology drives the large $\eta^{\prime}$ mass, and large-$N_c$ dynamics provide a unified framework for understanding SU($N_c$) gauge theories. The study underscores the power of non-perturbative lattice techniques to link hadron spectroscopy, topological structure, and color dynamics across dimensions and color numbers, while also highlighting areas where higher-precision 4D results are still needed.

Abstract

Lectures given at the Isaac Newton Institute, NATO-ASI School on "Confinement, Duality and Non-Perturbative Aspects of QCD", 23 June - 4 July, 1997.

Figures (14)

• Figure 1: The scalar glueball mass: the GF11 values ($\times$) and the rest ($\bullet$). The best linear extrapolation to the continuum limit is shown.
• Figure 2: The tensor glueball mass: the GF11 values ($\times$) and the rest ($\bullet$). The best linear extrapolation to the continuum limit is shown.
• Figure 3: The pseudoscalar glueball mass. The best linear extrapolation to the continuum limit is shown.
• Figure 4: The $\rho$ mass: GF11 ($\times$) and UKQCD ($\bullet$) values. The best linear extrapolations to the respective continuum limits are shown.
• Figure 5: The lattice topological charge: before cooling ($\times$) and after cooling ($\bullet$) the fields. Calculated on a sequence of fields separated by one Monte Carlo sweep.