Perfect Lattice Actions for Quarks and Gluons

TL;DR

This paper constructs perfect lattice actions for quarks and gluons using perturbation theory, identifying fixed point actions and vertex functions, and introduces a new renormalization group transformation for QCD.

Contribution

It develops a method to construct perfect lattice actions for quarks and gluons, including a new RG transformation extending results beyond perturbation theory.

Findings

Fixed point actions for free quarks and gluons obtained from continuum blocking.

Construction of classically perfect quark and gluon fields and operators.

Derivation of the quark-antiquark potential from the perfect Polyakov loop.

Abstract

We use perturbation theory to construct perfect lattice actions for quarks and gluons. The renormalized trajectory for free massive quarks is identified by blocking directly from the continuum. We tune a parameter in the renormalization group transformation such that for 1-d configurations the perfect action reduces to the nearest neighbor Wilson fermion action. The fixed point action for free gluons is also obtained by blocking from the continuum. For 2-d configurations it reduces to the standard plaquette action. Classically perfect quark and gluon fields, quark-gluon composite operators and vector and axial vector currents are constructed as well. Also the quark-antiquark potential is derived from the classically perfect Polyakov loop. The quark-gluon and 3-gluon perfect vertex functions are determined to leading order in the gauge coupling. We also construct a new block factor $n$ renormalization group transformation for QCD that allows to extend our results beyond perturbation theory. For weak fields it leads to the same perfect action as blocking from the continuum. For arbitrarily strong 2-d Abelian gauge fields the Manton plaquette action is classically perfect for this transformation.