Enlarged geometries of gauge bundles

TL;DR

This paper extends the geometric framework of gauge theories to include scenarios where gauge potentials do not behave as traditional connections, revealing new structures akin to torsion and gravitational effects in gauge models.

Contribution

It introduces a generalized geometric approach for gauge theories with non-connection gauge potentials, linking gauge deviations to spacetime torsion and gravitational phenomena.

Findings

Deformed gauge field-strength acts as torsion.

Generalized derivatives recover Bianchi identities.

Dynamical equations describe broken gauge models on curved spacetime.

Abstract

The geometrical picture of gauge theories must be enlarged when a gauge potential ceases to behave like a connection, as it does in electroweak interactions. When the gauge group has dimension four, the vector space isomorphism between spacetime and the gauge algebra is realized by a tetrad-like field. The object measuring the deviation from a strict bundle structure has the formal behavior of a spacetime connection, of which the deformed gauge field-strength is the torsion. A generalized derivative emerges in terms of which the two Bianchi identities are formally recovered. Effects of gravitational type turn up. The dynamical equations obtained correspond to a broken gauge model on a curved spacetime.