String models of glueballs and the spectrum of SU(N) gauge theories in 2+1 dimensions

TL;DR

The paper tests the Isgur-Paton flux-tube description of SU(N) glueballs in 2+1 dimensions by extending the model to include curvature/elasticity and short-distance physics, and by exploring mixing mechanisms that split the C=+ and C=− sectors. It introduces extra strings (N-ality), a curvature term γ_E, and short-distance corrections via F(ρ) or σ_eff(ρ), then fits the resulting spectra to lattice data for large N with two primary mixing scenarios: direct L↔R mixing and adjoint-string mixing. The main findings show that the C=+ sector is well reproduced, while 0^{-+} remains a significant discrepancy, possibly indicating a misidentification with a 4^{-+}; splittings require adjoint mixing (and possibly direct mixing) along with a nonzero curvature term, and the model predicts multiple SU(N→∞) mass towers that call for lattice data at higher masses to test. Overall, the results support a string-based view of glueballs in 2+1D and motivate refined lattice analyses to probe large-N towers and spin assignments.

Abstract

The spectrum of glueballs in 2+1 dimensions is calculated within an extended class of Isgur-Paton flux tube models and is compared to lattice calculations of the low-lying SU(N) glueball mass spectra. Our modifications of the model include a string curvature term and different ways of dealing with the flux tube width. We find that the generic model is remarkably successful at reproducing the positive charge conjugation, C=+, sector of the spectrum. The only large (and robust) discrepancy involves the 0-+ state. This raises the interesting possibility that the lattice spin identification is mistaken and that this state is in fact 4-+. In addition, the Isgur-Paton model does not incorporate any mechanism for splitting C=+ from C=- (in contrast to the case in 3+1 dimensions), while the `observed' spectrum shows a substantial splitting. We explore several modifications of the model in an attempt to incorporate this physics in a natural way. At the qualitative level we find that this constrains our choice to a picture in which the C=+/- splitting is driven by mixing with new states built on closed loops of adjoint flux. However a detailed numerical comparison suggests that a model incorporating an additional direct mixing between loops of opposite orientation is likely to work better; and that, in any case, a non-zero curvature term will be required. We also point out that a characteristic of any string model of glueballs is that the SU(N=infinity) mass spectrum will consist of multiple towers of states that are scaled up copies of each other. To test this will require a lattice mass spectrum that extends to somewhat larger masses than currently available.

Figures (3)

• Figure 1: Some of the observed SU($N$) $C=\pm$ splittings plotted versus $1/N^2$: the mass difference between the $0^{--}$ and the $0^{++}$ ($\bullet$) and that between the $2^{\pm -}$ and the $2^{\pm +}$ ($\circ$). As $N \to \infty$ the dependence is expected to be linear in $1/N^2$, i.e. like the straight lines added to the plot to guide the eye.
• Figure 2: The SU(2) $0^{+}$ mass ($\star$), the SU($N\geq 3$) $0^{++}$ masses ($\bullet$), the SU($N\geq 3$) $0^{--}$ masses ($\diamond$), and the average of the $0^{++}$ and $0^{--}$ masses ($\circ$), plotted against $1/N^2$; with the expected large-$N$ linear dependence shown in each case.
• Figure :