So(10) Heterotic M-Theory Vacua

Abstract

This talk adapts the available formalism to study a class of heterotic M-theory vacua with SO(10) grand unification group. Compactification to four dimensions with N = 1 supersymmetry is achieved on a torus fibered Calabi-Yau 3-fold Z = X/τX with first homotopy group π1(Z) = Z2. Here X is an elliptically fibered Calabi-Yau 3-fold which admits two global sections and τX is a freely acting involution on X. The vacua in this class have net number of three generations of chiral fermions in the observable sector and may contain M5-branes in the bulk space which wrap holomorphic curves in Z. Vacua with nonvanishing and vanishing instanton charges in the observable sector are considered. The latter case corresponds to potentially viable matter Yukawa couplings. Since π1(Z) = Z2, the grand unification group can be broken with Z2 Wilson lines.The motivation is to use the above formalism to extend realistic freefermionic models to the nonperturbative regime. The correspondence between these models and Z2 × Z2 orbifold compactification of the weakly coupled 10-dimensional heterotic string identifies associated Calabi-Yau 3-folds which possess the structure of the above Z and X. A nonperturbative extension of the top quark Yukawa coupling is discussed.