Renormalizability of a first principles Yang-Mills center-vortex ensemble

TL;DR

This paper proves the renormalizability of a nonperturbative Yang-Mills quantization method based on dividing configuration space into topological sectors, specifically the center-vortex sectors, which enhances the theoretical understanding of gauge theories.

Contribution

It provides a proof of renormalizability for the center-vortex sectors in Yang-Mills theory, supporting a new nonperturbative quantization approach.

Findings

Renormalizability is established for the center-vortex sectors.

Supports the calculability of the Yang-Mills center-vortex ensemble.

Addresses the Gribov problem in gauge fixing.

Abstract

Recently, a new procedure to quantize the $SU(N)$ Yang-Mills theory in the nonperturbative regime was proposed. The idea is to divide the configuration space $\{A_\mu\}$ into sectors labeled by different topological degrees of freedom and fix the gauge separately on each one of them. As Singer's theorem on gauge copies only refers to gauge fixing conditions that are global in $\{A_\mu\}$, this construction might avoid the Gribov problem. In this work, we present a proof of the renormalizability in the center-vortex sectors, thus establishing the calculability of the Yang-Mills center-vortex ensemble.