The classically perfect fixed point action for SU(3) gauge theory

TL;DR

This paper constructs fixed point actions for lattice SU(3) gauge theory that are classically perfect and potentially quantum perfect, eliminating cut-off effects in physical predictions and improving lattice simulations.

Contribution

It introduces a method to construct fixed point actions for SU(3) gauge theory that are both classically and potentially quantum perfect, reducing discretization errors.

Findings

Fixed point actions have scale invariant instanton solutions.

The quadratic spectrum of these actions is exact.

The q-qbar potential from fixed point operators shows no cut-off effects.

Abstract

In this paper (the first of a series) we describe the construction of fixed point actions for lattice $SU(3)$ pure gauge theory. Fixed point actions have scale invariant instanton solutions and the spectrum of their quadratic part is exact (they are classical perfect actions). We argue that the fixed point action is even 1--loop quantum perfect, i.e. in its physical predictions there are no $g^2 a^n$ cut--off effects for any $n$. We discuss the construction of fixed point operators and present examples. The lowest order $q {\bar q}$ potential $V(\vec{r})$ obtained from the fixed point Polyakov loop correlator is free of any cut--off effects which go to zero as an inverse power of the distance $r$.