Fixed point SU(3) gauge actions: scaling properties and glueballs

Abstract

We present a new parametrization of a SU(3) fixed point (FP) gauge action using smeared ("fat") gauge links. We report on the scaling behaviour of the FP action on coarse lattices by means of the static quark-antiquark potential, the hadronic scale r0, the string tension σ and the critical temperature Tc of the deconfining phase transition. In addition, we investigate the low lying glueball masses where we observe no scaling violations within the statistical errors.

Classically perfect gauge actions on anisotropic lattices

“…The classically perfect actions, described in principle by an infinite number of couplings, have to be parametrised in order to be suitable for numerical simulations. We have shown previously [28,40,41] that a parametrisation of the isotropic FP gauge action including APE-like smearing behaves much better and is much more flexible compared to common parametrisations using traces of closed loops with comparable computational cost. We thus decide to use an extension of this parametrisation to describe the anisotropic classically perfect gauge action.…”

“…The method has been introduced in [38] and it is presented in more detail in [39]. It relies upon a recent parametrisation of the isotropic classically perfect Fixed Point (FP) action [28,40,41] that includes a rich structure of operators as it is based on plaquettes built from simple gauge links as well as from smeared ("fat") links. We explicitly construct the ξ = 2 and 4 actions on coarse configurations typically occurring in Monte Carlo (MC) simulations.…”

“…In section 2 we describe our method of generating anisotropic perfect gauge actions without having to perform a certain number of renormalisation group transformations (RGT) leading from very fine to coarse lattices typical for MC simulations. Instead, we make use of the parametrisation of the isotropic FP action presented in [28,40,41]. We start with the isotropic parametrised FP action on rather large fluctuations and perform a small number of purely spatial blocking steps.…”

“…In practice the main advantage of applying one (or more) anisotropic spatial RGT is that we can directly start from a recent parametrisation of the isotropic FP gauge action [28,40,41] which is valid on rather coarse lattices. We can therefore avoid the cumbersome cascade procedure leading from very fine to coarser and coarser lattices.…”