  In the low energy domain of four-dimensional SU(2) Yang-Mills theory the spin
and the charge of the gauge field can become separated from each other. The
ensuing field variables describe the interacting dynamics between a version of
the O(3) nonlinear $\sigma$-model and a nonlinear Grassmannian $\sigma$-model,
both of which may support closed knotted strings as stable solitons. Lorentz
transformations act projectively in the O(3) model which breaks global internal
rotation symmetry and removes massless Goldstone bosons from the particle
spectrum. The entire Yang-Mills Lagrangian can be recast into a generally
covariant form with a conformally flat metric tensor. The result contains the
Einstein-Hilbert Lagrangian together with a nonvanishing cosmological constant,
and insinuates the presence of a novel dimensionfull parameter in the
Yang-Mills theory.
