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

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 $r$.