Sugawara-Sommerfield construction including canonical spin currents

Abstract

We set up the Sugawara-Sommerfield (SS) construction and generalize it by the inclusion of canonical spin current. Using the techniques of current algebra, we infer that the canonical spin current are linear in the vector-axial vector currents. From a geometric perspective, the underlying manifold has a vanishing Lorentz curvature and a non-vanishing torsion. This leads to teleparallelism and the canonical spin current (connection) assume a pure gauge form. Moreover, this model provides a possibility to unify gravity with strong-interactions by expressing the gravitational gauge connections in terms of the Yang-Mills gauge connections.