Weyl symmetric structure of QCD vacuum

TL;DR

This paper explores the Weyl symmetric structure of the QCD vacuum, revealing topological classifications and monopole solutions that suggest a Weyl symmetric vacuum may exist in quantum theory.

Contribution

It introduces a Weyl symmetric vacuum structure in SU(3) gauge theory using Killing vectors and topological classifications, including monopole solutions and their superpositions.

Findings

Classical vacuums classified by homotopy groups

Construction of Weyl sextet of vacuums

Finite energy monopole solutions including Weyl sextet

Abstract

We consider Weyl symmetric structure of the classical vacuum in quantum chromodynamics. In the framework of formalism of gauge invariant Abelian projection we show that classical vacuums can be constructed in terms of Killing vector fields on the group SU(3). Consequently, homotopic classes of Killing vector fields determine the topological structure of the vacuum. In particular, the second homotopy group \pi_2(SU(3)/U(1)\times U(1)) describes all topologically non-equivalent vacuums which are classified by two topological numbers. For each given Killing vector field one can construct six vacuums forming Weyl sextet representation. An interesting feature of SU(3) gauge theory is that it admits a Weyl symmetric vacuum represented by a linear superposition of the six vacuums from the Weyl vacuum sextet. A non-trivial manifestation of Weyl symmetry is demonstrated on monopole solutions. We construct a family of finite energy monopole solutions in Yang-Mills-Higgs theory which includes Weyl monopole sextet. From the analysis of the classical vacuum structure and monopole solutions we conjecture that a similar Weyl symmetric vacuum structure can be realized in quantum theory.