A class of two-dimensional Yang-Mills vacua and their relation to the non-linear sigma model

TL;DR

This paper explores classical vacuum solutions in 2D SU(2) Yang-Mills theory, revealing topologically non-trivial vacua linked to the non-linear O(3) model and particle motion in a periodic potential.

Contribution

It identifies a new class of topologically non-trivial vacua in 2D Yang-Mills theory and establishes their unexpected connection to the non-linear O(3) model.

Findings

Discovery of topologically non-trivial vacua in SU(2) Yang-Mills

Connection between Yang-Mills vacua and the non-linear O(3) model

Relation to particle motion in a periodic potential

Abstract

Classical vacuum - pure gauge - solutions of Euclidean two-dimensional SU(2) Yang-Mills theories are studied. Topologically non-trivial vacua are found in a class of gauge group elements isomorphic to $S_2$. These solutions are unexpectedly related to the solution of the non-linear O(3) model and to the motion of a particle in a periodic potential.