The intersecting brane world

TL;DR

This paper models the Standard Model scales using intersecting domain walls in a noncompact extra space, revealing geometric structures that determine particle localization and hierarchy.

Contribution

It introduces a novel geometric framework linking domain wall intersections, 1-cycle windings, and particle localization in extra-dimensional models.

Findings

Domain wall intersections correspond to particle locations.

The extra space is a covering space with specific topological properties.

Particles propagate on orthogonal 3-branes at intersection points.

Abstract

The scales of the Standard Model correspond to the positions of domain wall intersections on a straight line in a noncompact two-dimensional extra space. The domain walls partition an Anti-de Sitter spacetime. We show that domain wall intersections mark the orthogonal intersections of 1-cycles winding around a rectangular compact space and a hierarchy of subspaces, and that the noncompact extra space of the model is a covering space. 4-branes wrap 1-cycles of the compact spaces and intersect orthogonally in 3-branes, upon which the particles propagate. We show that particles are located precisely at domain wall intersections in the covering space.