Five-brane BPS states in heterotic M-theory

We present explicit methods for computing the discriminant curves and the a ssociated Kodaira type fiber degeneracies of elliptically fibered Calabi-Ya u threefolds. These methods are applied to a specific three-family, SU(5) g rand unified theory of particle physics within the context of Heterotic M-T heory. It is demonstrated that there is always a region of moduli space whe re a bulk space five-brane is wrapped on a pure fiber in the Calabi-Yau thr eefold. Restricting the discussion to the smooth parts of the discriminant curve, we explore the properties of the N = 2 BPS super-multiplets that ari se on the worldvolume of this five-brane due to the degeneration of the ell iptic fiber. The associated degenerating M membranes are shown to project t o string junctions in the base space. We use string junction techniques to explicitly compute the light BPS hyper- and vector multiplet spectrum for e ach Kodaira type fiber near the smooth part of the discriminant curve in th e SU(5) GUT theory.