Non-Split Geometry on Products of Vector Bundles

TL;DR

This paper introduces a novel geometric model for spliced vector bundles with multiple gauge structures, emphasizing non-splitting properties and complex interlacing of gauge interactions through advanced algebraic frameworks.

Contribution

It develops a new geometric framework for non-split spliced vector bundles using connection forms valued in product Lie algebras, highlighting the structure of the ghost sector and BRST algebra.

Findings

The model demonstrates non-splitting of the vector bundle geometry.

It characterizes the ghost sector as $x$-dependent deformations.

The BRST super algebra is derived from curvature invariance constraints.

Abstract

We propose a model in which a spliced vector bundle (with an arbitrary number of gauge structures in the splice) possesses a geometry which do not split. The model employs connection 1-forms with values in a space-product of Lie algebras, and therefore interlaces the various gauge structures in a non-trivial manner. Special attention is given to the structure of the geometric ghost sector and the super-algebra it possesses: The ghosts emerge as $x$-dependent deformations at the gauge sector, and the associated BRST super algebra is realized as constraints that follow from the invariance of the curvature.