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Spin-charge separation, conformal covariance and the $\text{SU}\left(2\right)$ Yang-Mills theory. (English) Zbl 1186.81086
Summary: In the low energy domain of four-dimensional $\text{SU}\left(2\right)$ 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 $\text{O}\left(3\right)$ 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 $\text{O}\left(3\right)$ 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.
##### MSC:
 81T13 Yang-Mills and other gauge theories