Yang-Mills theory in Landau gauge as a liquid crystal

TL;DR

This paper models SU(2) Yang-Mills theory in Landau gauge as a nematic liquid crystal, revealing topological defects like instantons and monopoles that influence its non-perturbative behavior.

Contribution

It introduces a novel analogy between Yang-Mills theory and liquid crystals using spin-charge separation, highlighting the role of topological defects in non-perturbative phenomena.

Findings

Yang-Mills ground state characterized by A^2 condensate

Topological defects include instantons, monopoles, vortices

Liquid crystal analogy offers new insights into non-perturbative effects

Abstract

Using a spin-charge separation of the gluon field in the Landau gauge we show that the SU(2) Yang-Mills theory in the low-temperature phase can be considered as a nematic liquid crystal. The ground state of the nematic crystal is characterized by the A^2 condensate of the gluon field. The liquid crystal possesses various topological defects (instantons, monopoles and vortices) which are suggested to play a role in non-perturbative features of the theory.