<A^2> Condensate, Bianchi Identities and Chromomagnetic Fields Degeneracy in SU(2) YM Theory

TL;DR

This paper investigates the violation of non-Abelian Bianchi identities and the role of degeneracy points in SU(2) Yang-Mills theory, linking these phenomena to confinement and topological sectors, and proposing a condensate explanation.

Contribution

It introduces a gauge-invariant, local formulation of Bianchi identities using physical fluxes, and explores their violation's impact on confinement and topology in SU(2) Yang-Mills theory.

Findings

Suppression of Bianchi identities violation may destroy confinement in 4D.

Removing degeneracy points leads to topologically non-trivial sectors.

The <A^2_{min}> condensate likely explains the observed phenomena.

Abstract

We consider the non-Abelian Bianchi identities in SU(2) pure Yang-Mills theory in D=3,4 focusing on the possibility of their violation and the significance of the chromomagnetic fields degeneracy points. We show that the recently proposed non-Abelian Stokes theorem allows to formulate the Bianchi identities in terms of the physical fluxes and their relative color orientations. Then the violation of Bianchi identities becomes a well defined concept ultimately related to the degeneracy points. The locality and gauge invariance of our approach allows to study the problem numerically. We present evidences that in D=4 the suppression of the Bianchi identities violation is likely to destroy confinement while the removal of the degeneracy points drives the theory to the topologically non-trivial sector. However, confronting the results obtained in three and four dimensions we argue that it is the mass dimension two condensate <A^2_{min}> which probably explains our findings.