Universality and scaling in SU(2) lattice gauge theory

Abstract

We calculate the lowest glueball masses and the string tension for both Manton's action and for Symanzik's tree-level improved action. We do so on large lattices and for small lattice spacings using techniques recently employed in an extensive investigation of the Wilson plaquette action. Comparing all these results we find that the ratios of the lightest masses are universal to a high degree of accuracy. In particular, we confirm that on large volumes the tensor glueball is heavier than the scalar glueball: m[2 +]⋍1.5 m[0 +] . We repeat these calculations for larger lattice spacings and find that the string tension follows 2-loop perturbation theory more closely in the case of these alternative actions than in the case of the standard plaquette action. Our attempt to repeat the analysis with Wilson's block-spin improved action foundered on the strong breakdown of positivity apparent in the calculated correlation functions. In all cases which we were able to study the observed violations of scaling are in the same direction. This suggests that the causes of the scaling violations observed with Wilson's plaquette action are “semi-universal”. It also weakens the implication of the observed universality for the question of how close we are to the continuum limit.