SU(N) gauge theories in 2+1 dimensions -- further results

TL;DR

This study extends the large-$N_c$ analysis of SU($N_c$) gauge theories in 2+1 dimensions by incorporating new SU(4) and SU(6) lattice data alongside earlier N=2–5 results to refine $N_c \to \infty$ extrapolations with fixed $\lambda=g^2N_c$. It confirms persistent linear confinement at large $N_c$ with leading corrections of $O(1/N_c^2)$ and shows glueball masses depend only weakly on $N_c$, with no clear evidence for a proliferation of states from closed flux loops in the accessible spectrum. The work provides quantitative benchmarks for analytic large-$N$ methods and supports compatibility with both Dalley’s large-$N$ glueball predictions and AdS/CFT results. Overall, it reinforces the robustness of the large-$N$ picture in 2+1 dimensions and clarifies the role of flux-loops in the glueball spectrum.

Abstract

We calculate the string tension and part of the mass spectrum of SU(4) and SU(6) gauge theories in 2+1 dimensions using lattice techniques. We combine these new results with older results for N=2,...,5 so as to obtain more accurate extrapolations to N=infinity. The qualitative conclusions of the earlier work are unchanged: SU(N) theories in 2+1 dimensions are linearly confining as N->infinity; the limit is achieved by keeping g.g.N fixed; SU(3), and even SU(2), are `close' to SU(infinity). We obtain more convincing evidence than before that the leading large-N correction is O(1/N.N). We look for the multiplication of states that one expects in simple flux loop models of glueballs, but find no evidence for this.

Figures (4)

• Figure 1: The mass of a periodic flux loop of length $aL$ at $\beta=28$ in SU(4). The line shows a fit of the form in eqn(\ref{['C1']}).
• Figure 2: The value of $\surd\sigma/g^2$ as a function of $N_c$. The line shows the fit in eqn(\ref{['C12']}).
• Figure 3: The $\chi^2$ per degree of freedom against the power, $\alpha$, of the leading large-$N_c$ correction when fitting $\surd\sigma/g^2N_c$ to eqn(\ref{['C4']}).
• Figure 4: $0^{++}$($\bullet$) and $0^{--}$($\times$) glueball masses in units of $g^2N_c$, plotted against $1/N_c^2$. The best linear extrapolations to the $N_c = \infty$ limit are shown.