Stable vector bundles and string theory

Abstract

In [4], Braim, He, Ovrut and Pantev proposed a model of string theory (based on the Calabi-Yau 3-fold X defined in [3]) whose low energy limit predicts certain properties of the Standard Model of particle Physics. This model depends on two vector bundles that have to be stable. We calculate the ample cone of X, and prove that one of them is stable, and the other one is not.