Chromo-electric Yang-Mills gauge fields

TL;DR

This paper constructs static chromo-electric gauge field configurations in SU(2), SU(3), and SU(4) Yang-Mills theories, revealing new vacuum solutions that differ from the trivial vacuum.

Contribution

It introduces a systematic method to generate static chromo-electric configurations for SU(N) gauge theories by embedding SU(2) Lie algebra structures, extending previous approaches.

Findings

Constructed static chromo-electric configurations for SU(2), SU(3), and SU(4)

Discovered gauge-inequivalent vacuum solutions different from the trivial vacuum

Provided a straightforward generalization method for SU(N) with N>2

Abstract

We obtain static gauge field configurations for SU(2) Yang-Mills gauge theory in the absence of chromo-magnetic field. We also present a systematic way to obtain such configurations for SU(3) and SU(4) YM gauge theories by realizing their Lie algebras in terms of SU(2). Generalization of our method to SU(N) gauge theory with N>2 is straight forward. The gauge fields thus obtained are complex. We investigated the issue of uniform as well as real chromo-electric field with these configurations. Furthermore, we investigated the possible class of vacuum solutions for the gauge fields and found that they are gauge inequivalent to the usual vacuum configuration $A^a_{\mu}=0$.