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

TL;DR

This paper constructs specific N=1 supersymmetric vacua in heterotic M-theory with SO(10) symmetry, three generations, and viable Yukawa couplings, extending perturbative calculations to the nonperturbative regime.

Contribution

It demonstrates the existence of a new class of heterotic M-theory vacua with realistic features and proposes a method to compute Yukawa couplings nonperturbatively.

Findings

Existence of vacua with SO(10) symmetry and three generations.

Potential for viable matter Yukawa couplings.

Extension of Yukawa coupling calculations to nonperturbative regime.

Abstract

We demonstrate the existence of a class of N=1 supersymmetric nonperturbative vacua of Horava-Witten M-theory compactified on a torus fibered Calabi-Yau 3-fold Z with first homotopy group \pi_{1}(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 V_{Z} 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 Horava-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 X Z2 orbifold without resorting to the full three generation models.