Connections and Generalized Gauge Transformations

TL;DR

This paper explores how gauge transformations and fiber bundle structures relate to supergravity and superstring theories, proposing geometric principles for gauge interactions, unification, and anomaly cancellation in fundamental physics.

Contribution

It introduces a geometric framework connecting fiber bundle reductions, gauge groups, and superstring theory, emphasizing the role of division algebras and fermions in unification.

Findings

Reduction of structure group via fiber coordinate elimination.

Application of nonlinear SU(4) action to supergravity and string theory.

Proposal of a geometric mechanism for anomaly cancellation.

Abstract

Elimination of the fibre coordinate dependence from the connection form transformation rule for a bundle with a coset manifold standard fibre reduces the structure group. The nonlinear SU(4) action on an $S^7$ bundle is applied to the dimensional reduction of eleven-dimensional supergravity and ten-dimensional superstring theory to four dimensions. A principle, consistent with higher-dimensional superstring theory, is suggested to explain the types of gauge interactions that arise in the standard model based on the geometry of the internal symmetry spaces. It is shown why a Lie group structure is required for vector bosons in pure gauge theories and that the application of division algebras to force unification must begin with the fermions comprising the elementary particle multiplets of the standard model. A suggestion is made for establishing a mechanism for the cancellation of anomalies within this approach to superstring theory.