SO(10) heterotic M-theory vacua

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 Mold Z = X/tau(X) with first homotopy group pi(1) (Z) = Z(2). Here X is an elliptically fibered Calabi-Yau 3-fold which admits two global sections and tau(X) 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 pi(1) (Z) = Z(2), the grand unification group can be broken with Z(2) Wilson lines. The motivation is to use the above formalism to extend realistic free-fermionic models to the nonperturbative regime. The correspondence between these models and Z(2) X Z(2) 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.