Bianchi Identities and Degeneracy of Chromomagnetic Fields in SU(2) Gluodynamics

TL;DR

This paper explores the role of Bianchi identities and chromomagnetic field degeneracy in SU(2) lattice Yang-Mills theory, revealing their impact on confinement and topological sectors.

Contribution

It introduces a formulation of Bianchi identities using local fluxes and links their violation and degeneracy points to confinement and topological properties.

Findings

Violation suppression destroys confinement in 4D

Removing degeneracy points leads to topologically non-trivial sectors

Numerical evidence supports the connection between Bianchi violations and confinement

Abstract

We investigate the non-Abelian Bianchi identities in pure SU(2) lattice Yang-Mills theory in three and four dimensions. The non-Abelian Stokes theorem proposed recently allows to formulate the Bianchi identities in terms of local physical fluxes. Then the violation of Bianchi identities becomes a well defined concept ultimately related to chromomagnetic fields degeneracy points. We present numerical evidences that in D=4 the suppression of the Bianchi identities violation destroys confinement while the removal of the degeneracy points drives the theory to the topologically non-trivial sector.