The Grassmannian Sigma Model in SU(2) Yang-Mills Theory

TL;DR

This paper constructs a Grassmannian sigma model within SU(2) Yang-Mills theory using quaternionic decomposition, clarifying its role in spin-charge separation phenomena.

Contribution

It explicitly formulates the Grassmannian sigma model relevant to SU(2) Yang-Mills theory via quaternionic methods, confirming its significance in spin-charge separation.

Findings

Explicit construction of the Grassmannian sigma model

Verification of its relevance in SU(2) Yang-Mills spin-charge separation

Discussion of coupling with the O(3) sigma model

Abstract

Spin-charge separation in pure SU(2) Yang-Mills theory was recently found to involve the dynamics of an O(3) non-linear sigma model and, seemingly, a Grassmannian non-linear sigma model. In this article we explicitly construct the Grassmannian sigma model of the form appearing in the the spin-charge separated SU(2) theory through a quaternionic decomposition of the manifold, thus verifying its relevance in this context. The coupling between this model and the O(3) non-linear sigma model is further commented upon.