Large Nc physics from the lattice

TL;DR

The paper uses fully nonperturbative lattice gauge theory to test large-$N_c$ QCD, confirming a smooth limit as $N_c\to\infty$ when the 't Hooft coupling $\lambda=g^2N_c$ is held fixed. It presents continuum-extrapolated results for glueball masses, the running coupling, and $k$-string tensions across $N_c=2$–$5$, showing $N_c=3$ is already close to the infinite-$N_c$ regime for many quantities. A key finding is that $k$-strings are strongly bound and that their tensions approach, or lie between, MQCD and Casimir-scaling predictions, implying nonperturbative effects can induce $O(1/N_c)$ corrections. The work also discusses topology and the deconfining transition, highlighting a robust, confining large-$N_c$ limit with practical implications for modeling QCD at finite $N_c$. Overall, the results validate large-$N_c$ techniques and reveal nonperturbative structures that modify naive color counting.

Abstract

I summarise what lattice methods can contribute to our understanding of the phenomenology of QCD at large Nc and describe some recent work on the physics of SU(Nc) gauge theories. These non-perturbative calculations show that there is indeed a smooth Nc -> infinity limit and that it is achieved by keeping g.g.Nc fixed, confirming the usual diagrammatic analysis. The lattice calculations support the crucial assumption that the theory remains linearly confining at large Nc. Moreover we see explicitly that Nc=3 is `close to' Nc=infinity for many physical quantities. We comment on the fate of topology and the deconfining transition at large Nc. We find that multiple confining strings are strongly bound. The string tensions, K(k), of these k-strings are close to the M(-theory)QCD-inspired conjecture as well as to `Casimir scaling' with the most accurate recent calculations favouring the former. We point out that closed k-strings provide a natural way for non-perturbative effects to introduce O(1/Nc) corrections into the pure gauge theory, in contradiction to the conventional diagrammatic expectation.

Figures (5)

• Figure 1: SU(4) correlation function for the $0^{++}$ glueball; exponential fit shown.
• Figure 2: The lightest SU(4) scalar glueball mass, $m_{0^{++}}$, expressed in units of the string tension, $\sigma$, plotted against the latter in lattice units. The $a\to 0$ continuum extrapolation, using a leading lattice correction, is shown.
• Figure 3: The mass of the lightest scalar glueball, $m_{0^{++}}$, .... expressed in units of the string tension, $\sigma$, is plotted against $1/N^2_c$. The $N_c\to \infty$ extrapolation is shown.
• Figure 4: 't Hooft coupling at the scale $a$ in physical units.
• Figure 5: $k=2$ string tensions in SU(4) ($\bullet$) and SU(5) ($\circ$).