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

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 ≥ 2) glueball mass spectrum. 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 the 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 → ∞) 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.