Fixed point actions for SU(3) gauge theory

TL;DR

This paper discusses the development of fixed point actions for lattice SU(3) gauge theory that eliminate certain discretization errors and demonstrate improved scaling behavior compared to Wilson actions.

Contribution

The authors construct a classical fixed point action for SU(3) gauge theory with scale-invariant instanton solutions and verify its superior scaling properties through numerical tests.

Findings

Fixed point actions have no cut-off effects in physical predictions.

The approximate fixed point action scales within statistical errors for aT_c ≤ 1/2.

Wilson action shows about 10% scaling violations.

Abstract

We summarize our recent work on the construction and properties of fixed point (FP) actions for lattice $SU(3)$ pure gauge theory. These actions have scale invariant instanton solutions and their spectrum is exact through 1--loop, i.e. in their physical predictions there are no $a^n$ nor $g^2 a^n$ cut--off effects for any $n$. We present a few-parameter approximation to a classical FP action which is valid for short correlation lengths. We perform a scaling test of the action by computing the quantity $G = L \sqrt{\sigma(L)}$, where the string tension $\sigma(L)$ is measured from the torelon mass $\mu = L \sigma(L)$, on lattices of fixed physical volume and varying lattice spacing $a$. While the Wilson action shows scaling violations of about ten per cent, the approximate fixed point action scales within the statistical errors for $ 1/2 \ge aT_c$.