The Sugawara-Sommerfield construction including canonical spin current

TL;DR

This paper extends the Sugawara-Sommerfield construction by incorporating canonical spin currents, revealing geometric structures with torsion and exploring potential unification of gravity and strong interactions through gauge connections.

Contribution

It generalizes the SS construction to include canonical spin currents and links geometric torsion with gauge theories, suggesting a pathway to unify gravity with strong interactions.

Findings

Canonical spin currents are linear in vector-axial vector currents.

Underlying manifold exhibits vanishing Lorentz curvature with non-zero torsion.

Model suggests a geometric unification of gravity and strong interactions.

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.