QCD_4 From a Five-Dimensional Point of View

TL;DR

This paper introduces a 5-dimensional topological quantum field theory framework for 4D Yang-Mills theory, linking perturbative and non-perturbative aspects and proposing a new Monte-Carlo algorithm with improved properties.

Contribution

It presents a novel 5D formulation of 4D Yang-Mills theory, enabling renormalization at finite orders and a new Monte-Carlo approach based on the fifth dimension.

Findings

A well-defined 5D topological quantum field theory for Yang-Mills.

A lattice expression for new fields in topological Yang-Mills.

A critical limit for correlation functions and auto-correlations.

Abstract

We propose a 5-dimensional definition for the physical 4D-Yang-Mills theory. The fifth dimension corresponds to the Monte-Carlo time of numerical simulations of QCD_4. The 5-dimensional theory is a well-defined topological quantum field theory that can be renormalized at any given finite order of perturbation theory. The relation to non-perturbative physics is obtained by expressing the theory on a lattice, a la Wilson. The new fields that must be introduced in the context of a topological Yang-Mills theory have a simple lattice expression. We present a 5-dimensional critical limit for physical correlation functions and for dynamical auto-correlations, which allows new Monte-Carlo algorithm based on the time-step in lattice units given by $\e = g_0^{-13/11}$ in pure gluodynamics. The gauge-fixing in five dimensions is such that no Gribov ambiguity occurs. The weight is strictly positive, because all ghost fields have parabolic propagators and yield trivial determinants. We indicate how our 5-dimensional description of the Yang-Mills theory may be extended to fermions.