Five-Brane BPS States in Heterotic M-Theory

TL;DR

This paper develops methods to analyze elliptic fibrations in Calabi-Yau threefolds, applies them to a heterotic M-theory GUT model, and computes BPS spectra associated with five-branes and fiber degenerations.

Contribution

It introduces explicit techniques for discriminant and fiber analysis in elliptic Calabi-Yau threefolds within heterotic M-theory, focusing on five-brane configurations and BPS spectra.

Findings

Existence of regions with five-branes wrapped on pure fibers.

Explicit computation of BPS hyper- and vector multiplet spectra.

Connection between fiber degenerations and string junctions.

Abstract

We present explicit methods for computing the discriminant curves and the associated Kodaira type fiber degeneracies of elliptically fibered Calabi-Yau threefolds. These methods are applied to a specific three-family, SU(5) grand unified theory of particle physics within the context of Heterotic M-Theory. It is demonstrated that there is always a region of moduli space where a bulk space five-brane is wrapped on a pure fiber in the Calabi-Yau threefold. Restricting the discussion to the smooth parts of the discriminant curve, we explore the properties of the N=2 BPS supermultiplets that arise on the worldvolume of this five-brane due to the degeneration of the elliptic fiber. The associated degenerating M membranes are shown to project to string junctions in the base space. We use string junction techniques to explicitly compute the light BPS hyper- and vector multiplet spectrum for each Kodaira type fiber near the smooth part of the discriminant curve in the SU(5) GUT theory.