Particle theory

Abstract:

We compute glueball masses for even spins ranging from 0 to 6, in the D = 2 + 1 SU(2) lattice gauge theory. We do so over a wide range of lattice spacings, and this allows a well-controlled extrapolation to the continuum limit. When the resulting spectrum is presented in the form of a Chew-Frautschi plot we find that we can draw a straight Regge trajectory going through the lightest glueballs of spin 0, 2, 4 and 6. The slope of this trajectory is small and turns out to lie between the predictions of the adjoint-string and flux-tube glueball models. The intercept we find, α0∼-1, is much lower than is needed for this leading trajectory to play a 'Pomeron-like' role of the kind it is often believed to play in D = 3 + 1. We elaborate the Regge theory of high-energy scattering in 2 space dimensions, and we conclude, from the observed low intercept, that high-energy glueball scattering is not dominated by the leading Regge pole exchange, but rather by a more complex singularity structure in the region 0≤Reλ≤1/2 of the complex angular momentum λ plane. We show that these conclusions do not change if we go to larger groups, SU(N>2), and indeed to SU(∞), and we contrast all this with our very preliminary calculations in the D = 3 + 1 SU(3) gauge theory. © 2003 Elsevier B.V. All rights reserved.

Abstract:

We study the Polyakov line in Yang-Mills matrix models, which include the IKKT model of IIB string theory. For the gauge group SU(2) we give the exact formulae in the form of integral representations which are convenient for finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper bounds which decay as a power law at large momentum p. We argue that these capture the full asymptotic behaviour. We also indicate how to extend the results to some correlation functions of Polyakov lines.