Yukawa couplings in SO(10) heterotic M-theory vacua Original Research Article

We demonstrate the existence of a class of N=1 supersymmetric nonperturbative vacua of Hořava–Witten M-theory compactified on a torus fibered Calabi–Yau 3-fold Z with first homotopy group π1(Z)=Z2, having the following properties: (1) SO(10) grand unification group, (2) net number of three generations of chiral fermions in the observable sector, and (3) potentially viable matter Yukawa couplings. These vacua correspond to semistable holomorphic vector bundles VZ over Z having structure group SU(4)C, and generically contain M5-branes in the bulk space. The nontrivial first homotopy group allows Wilson line breaking of the SO(10) symmetry. Additionally, we propose how the 11-dimensional Hořava–Witten M-theory framework may be used to extend the perturbative calculation of the top quark Yukawa coupling in the realistic free-fermionic models to the nonperturbative regime. The basic argument being that the relevant coupling couples twisted–twisted–untwisted states and can be calculated at the level of the Z2×Z2 orbifold without resorting to the full three generation models.