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

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.Comment: 24 pages. Standard LaTe

On the Possibility of Optical Unification in Heterotic Strings

Recently J. Giedt discussed a mechanism, entitled optical unification, whereby string scale unification is facilitated via exotic matter with intermediate scale mass. This mechanism guarantees that a virtual MSSM unification below the string scale is extrapolated from the running of gauge couplings upward from M_Z^o when an intermediate scale desert is assumed. In this letter we explore the possibility of optical unification within the context of weakly coupled heterotic strings. In particular, we investigate this for models of free fermionic construction containing the NAHE set of basis vectors. This class is of particular interest for optical unification, because it provides a standard hypercharge embedding within SO(10), giving the standard k_Y = 5/3 hypercharge level, which was shown necessary for optical unification. We present a NAHE model for which the set of exotic SU(3)_C triplet/anti-triplet pairs, SU(2)_L doublets, and non-Abelian singlets with hypercharge offers the possibility of optical unification. Whether this model can realize optical unification is conditional upon these exotics not receiving Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum expectation values is non-perturbatively chosen to cancel the FI D-term, xi, generated by the anomalous U(1)-breaking Green-Schwarz-Dine-Seiberg-Wittten mechanism. A study of perturbative flat directions and their phenomenological implications for this model is underway. This paper is a product of the NFS Research Experiences for Undergraduates and the NSF High School Summer Science Research programs at Baylor University.Comment: 16 pages. Standard Late

Investigation of Quasi--Realistic Heterotic String Models with Reduced Higgs Spectrum

Quasi--realistic heterotic-string models in the free fermionic formulation typically contain an anomalous U(1), which gives rise to a Fayet-Iliopolous term that breaks supersymmetry at the one--loop level in string perturbation theory. Supersymmetry is restored by imposing F- and D-flatness on the vacuum. In Phys. Rev. D 78 (2008) 046009, we presented a three generation free fermionic standard-like model which did not admit stringent F- and D-flat directions, and argued that the all the moduli in the model are fixed. The particular property of the model was the reduction of the untwisted Higgs spectrum by a combination of symmetric and asymmetric boundary conditions with respect to the internal fermions associated with the compactified dimensions. In this paper we extend the analysis of free fermionic models with reduced Higgs spectrum to the cases in which the SO(10) symmetry is left unbroken, or is reduced to the flipped SU(5) subgroup. We show that all the models that we study in this paper do admit stringent flat directions. The only examples of models that do not admit stringent flat directions remain the strandard-like models of reference Phys. Rev. D 78 (2008) 046009.Comment: 38 pages, 1 figur

Minimal Standard Heterotic String Models

Three generation heterotic-string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable Standard Model charged sector. The relation of these models to Z_2 x Z_2 orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, that give superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions and hence directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.Comment: 20 pages, LaTeX; added reference

A Minimal Superstring Standard Model I: Flat Directions

Three family SU(3)_C x SU(2)_L x U(1)_Y string models in several constructions generically possess two features: (i) an extra local anomalous U(1)_A and (ii) numerous (often fractionally charged) exotic particles beyond those in the minimal supersymmetric model (MSSM). Recently, we demonstrated that the observable sector effective field theory of such a free fermionic string model can reduce to that of the MSSM, with the standard observable gauge group being just SU(3)_C x SU(2)_L x U(1)_Y and the SU(3)_C x SU(2)_L x U(1)_Y-charged spectrum of the observable sector consisting solely of the MSSM spectrum. An example of a model with this property was shown. We continue our investigation of this model by presenting a large set of different flat directions of the same model that all produce the MSSM spectrum. Our results suggest that even after imposing the conditions for the decoupling of exotic states, there may remain sufficient freedom to satisfy the remaining phenomenological constraints imposed by the observed data.Comment: 64 pages. Latex. Revisions to match version in Int. J. Mod. Physics

Phenomenology of A Three-Family Standard-like String Model

We discuss the phenomenology of a three-family supersymmetric Standard-like Model derived from the orientifold construction, in which the ordinary chiral states are localized at the intersection of branes at angles. In addition to the Standard Model group, there are two additional U(1)' symmetries, one of which has family non-universal and therefore flavor changing couplings, and a quasi-hidden non-abelian sector which becomes strongly coupled above the electroweak scale. The perturbative spectrum contains a fourth family of exotic (SU(2)- singlet) quarks and leptons, in which, however, the left-chiral states have unphysical electric charges. It is argued that these decouple from the low energy spectrum due to hidden sector charge confinement, and that anomaly matching requires the physical left-chiral states to be composites. The model has multiple Higgs doublets and additional exotic states. The moduli-dependent predictions for the gauge couplings are discussed. The strong coupling agrees with experiment for reasonable moduli, but the electroweak couplings are too small.Comment: 22 pages, 4 figure