How Self-Dual is QCD?

TL;DR

This paper investigates the extent of self-duality in the vacuum of pure-glue SU(3) gauge theory using lattice methods, finding a small but positive tendency towards self-duality.

Contribution

It introduces a method to decompose gauge fields into self-dual and anti-self-dual parts and applies polarization analysis to quantify vacuum self-duality in lattice gauge theory.

Findings

Evidence of a small positive dynamical tendency for self-duality in the vacuum.

The tendency towards self-duality diminishes in the continuum limit.

Methodology can be applied to other gauge theories to study vacuum structure.

Abstract

Vacuum characteristics quantifying dynamical tendency toward self-duality in gauge theories could be used to judge the relevance of classical solutions or the viability of classically motivated vacuum models. Here we decompose the field strength of equilibrium gauge configurations into self-dual and anti-self-dual parts, and apply absolute X-distribution method to the resulting polarization dynamics in order to construct such characteristics. Using lattice regularization and focusing on pure-glue SU(3) gauge theory at zero temperature, we find evidence for positive but very small dynamical tendency for self-duality of vacuum in the continuum limit.