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

Abstract

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 π 1 (Z) = Z 2 , 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 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 Z 2 × Z 2 orbifold without resorting to the full three generation models. * faraggi@thphys.ox.ac.uk

So(10) Heterotic M-Theory Vacua

“…4 N gen = 3, H = SO(10) vacua N gen = 3, H = SO(10) heterotic M-theory vacua with nonvanishing and vanishing instanton charges in the observable sector are searched for in [13] and [14], respectively. In the former work, the search is restricted to vector bundles satisfying the Class A or Class B constraints: where m ∈ Z.…”

“…The new results presented in this talk have been published by Faraggi, Garavuso and Isidro [13] and Faraggi and Garavuso [14]. Section 2 reviews realistic free-fermionic models and their Z 2 × Z 2 correspondence, explains the connection [13] with the Calabi-Yau 3-folds Z and X, and offers a proposal to obtain a nonperturbative extension [14] of the top quark Yukawa coupling calculation flipped SU (5) [15].…”

“…Section 2 reviews realistic free-fermionic models and their Z 2 × Z 2 correspondence, explains the connection [13] with the Calabi-Yau 3-folds Z and X, and offers a proposal to obtain a nonperturbative extension [14] of the top quark Yukawa coupling calculation flipped SU (5) [15]. We will see that, although the precise geometrical realization of the full N gen = 3 models is unknown, this coupling can be computed as a 27 3 E 6 or 16 · 16 · 10 SO(10) coupling with N gen = 24.…”

“…This leads us to present rules for constructing heterotic M-theory vacua allowing H = E 6 and SO(10) grand unification groups with arbitrary N gen . Section 3 summarizes rules [14] allowing grand unification groups H = E 6 , SO (10), and SU (5), corresponding to G = SU (n) with n = 3, 4, and 5, respectively. As discussed by Arnowitt and Dutta [16], requiring vanishing instanton charges in the observable sector yields potentially viable matter Yukawa couplings.…”

“…As discussed by Arnowitt and Dutta [16], requiring vanishing instanton charges in the observable sector yields potentially viable matter Yukawa couplings. N gen = 3, H = SO(10) vacua with nonvanishing [13] and vanishing [14] instanton charges in the observable sector are discussed in Section 4.…”