String models of glueballs and the spectrum ofSU(N)gauge theories in2+1dimensions

Abstract

Abstract.The spectrum of glueballs in 2+1 dimensions is calculated within an extended class of Isgur-Paton flux tube models and 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 a new way of dealing with the short-distance cut-off. 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, raising the interesting possibility that the lattice spin identification is mistaken and that this state is in fact 4 −+ . Additionally, 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 does show 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.

High Spin Glueballs From the Lattice

“…Moreover the latter mass is close to the mass of the 4 − glueball as predicted by the flux tube model [4,6]. Since the A 2 lattice representation contains the continuum 0 − , 4 − , .…”

“…As remarked in the Introduction, a robust prediction [4,6] of the Isgur-Paton flux tube model [2] is that the lightest 0 − state should be much heavier than the mass that has been obtained in lattice calculations [9] of the lightest SU(2) glueball in the A 2 lattice representation. Moreover the latter mass is close to the mass of the 4 − glueball as predicted by the flux tube model [4,6].…”

“…(19) how the finite volume affects the quantity ∆. (6,8) and (10,0); the asymptotic value for infinite volume is indicated as a constant Due to "paths around the world", significant finite volume effects are seen when looking at the difference between superlinks of same Euclidean length, pointing in different directions.…”

Hagedorn transition, vortices and D0 branes: lessons from 2+1 confining strings

“…Strong coupling corresponds to the pure Yang Mills theory. In this case, at least at large N the spectrum is believed to be much closer to a stringy spectrum [39]. So perhaps the Hagedorn transition takes over.…”

Improved superlinks for higher spin glueballs

“…The timeslice overlap between the operators is identified by the value of t in Equation (5). We restrict ourselves in this article to using loops which are π-symmetric-if we were to use closed loops which were not symmetric under a rotation by π, we could recover both even and odd spins and both positive and negative parity, otherwise phase cancellations restrict us to the positive-parity, even-spin sector of the spectrum.…”