Landscape of QCD Vacuum

TL;DR

This paper explores new gauge field solutions in QCD that form a complex landscape of vacuum states, potentially explaining CP symmetry restoration through tunneling between different configurations.

Contribution

It introduces novel solutions of the Yang-Mills equations representing a condensate of chromomagnetic vortices, revealing a complex vacuum landscape in QCD.

Findings

Solutions describe chromomagnetic vortex condensates

Potential barriers form a complex vacuum landscape

Tunneling may restore CP symmetry dynamically

Abstract

We found new solutions of the sourceless Yang-Mills equation describing the superposition of chromomagnetic vortices of oppositely oriented magnetic fluxes. These gauge field configurations have constant energy densities and are separated by potential barriers forming a complicated landscape. It is suggested that the solutions describe the condensate of chromomagnetic vortices and represent a dual analog of the Cooper pairs condensate in a superconductor. In the presence of an Abelian field and in a particular limit the solutions reduce to the flat connections of zero energy density and are forming a complicated potential landscape of the QCD vacuum. A possible tunnelling transition between these superfluxon flat configurations and the flat configurations with non-vanishing Chern-Pontryagin index will wash out the CP violating $\theta$ angle to zero, dynamically restoring CP symmetry.