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

Initial Systematic Investigations of the Landscape of Low Layer NAHE Extensions

The discovery that the number of physically consistent string vacua is on the order of 10^500 has prompted several statistical studies of string phenomenology. Contained here is one such study that focuses on the Weakly Coupled Free Fermionic Heterotic String (WCFFHS) formalism. Presented are systematic extensions of the well-known NAHE (Nanopoulos, Antoniadis, Hagelin, Ellis) set of basis vectors, which have been shown to produce phenomenologically realistic models. Statistics related to the number of U(1)'s, gauge group factors, non-Abelian singlets, ST SUSYs, as well as the gauge groups themselve are discussed for the full range of models produced as well as models containing GUT groups only. Prior results of other large-scale investigations are compared with these regarding the aforementioned quantities. Statistical coupling between the gauge groups and the number of ST SUSYs is also discussed, and it was found that for order-3 extensions there are more models with enhanced ST SUSY when there is an exceptional group present. Also discussed are some three-generation GUT models found in the data sets. These models are unique because they come from basis vectors which still have a geometric interpretation -- there are no "rank-cuts" in these models.Comment: 65 Pages, 31 Tables, 31 Figure

Left-Right Symmetric Heterotic-String Derived Models

Recently it was demonstrated that free fermionic heterotic-strings can produce models with solely the Minimal Supersymmetric Standard Model states in the low energy spectrum. This unprecedented result provides further strong evidence for the possibility that the true string vacuum shares some of the properties of the free fermionic models. Past free fermionic models have focused on several possible unbroken observable SO(10) subgroups at the string scale, which include the flipped SU(5) (FSU5), the Pati-Salam (PS) string models, and the string Standard-like Models (SLM). We extend this study to include the case in which the SO(10) symmetry is broken to the Left-Right Symmetric (LRS) gauge group, SO(10) -> SU(3)_C X U(1)_{B-L} X SU(2)_L X SU(2)_R. We present several models of this type and discuss their phenomenological features. The most striking new outcome of the LRS string models, in contrast to the case of the FSU5, the PS, and the SLM string models, is that they can produce effective field theories that are free of Abelian anomalies. We discuss the distinction between the two types of free fermionic models which result in the presence, or absence, of an anomalous U(1). As a counter example we also present a LRS model that does contain an anomalous U(1). Additionally, we discuss how in string models the Standard Model spectrum may arise from the three \mbf 16 representations of SO(10), while the weak-hypercharge does not have the canonical SO(10) embedding.Comment: 39 pages. Standard Latex. Version to appear in PR

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

Nematic liquid crystal alignment on chemical patterns

Patterned Self-Assembled Monolayers (SAMs) promoting both homeotropic and planar degenerate alignment of 6CB and 9CB in their nematic phase, were created using microcontact printing of functionalised organothiols on gold films. The effects of a range of different pattern geometries and sizes were investigated, including stripes, circles and checkerboards. EvanescentWave Ellipsometry was used to study the orientation of the liquid crystal (LC) on these patterned surfaces during the isotropic-nematic phase transition. Pretransitional growth of a homeotropic layer was observed on 1 ¹m homeotropic aligning stripes, followed by a homeotropic mono-domain state prior to the bulk phase transition. Accompanying Monte-Carlo simulations of LCs aligned on nano-patterned surfaces were also performed. These simulations also showed the presence of the homeotropic mono-domain state prior to the transition.</p

Computer simulations of hard pear-shaped particles

We report results obtained from Monte Carlo simulations investi- gating mesophase formation in two model systems of hard pear-shaped particles. The first model considered is a hard variant of the trun- cated Stone-Expansion model previously shown to form nematic and smectic mesophases when embedded within a 12-6 Gay-Berne-like po- tential [1]. When stripped of its attractive interactions, however, this system is found to lose its liquid crystalline phases. For particles of length to breadth ratio k = 3, glassy behaviour is seen at high pressures, whereas for k = 5 several bi-layer-like domains are seen, with high intradomain order but little interdomain orientational correlation. For the second model, which uses a parametric shape parameter based on the generalised Gay-Berne formalism, results are presented for particles with elongation k = 3; 4 and 5. Here, the systems with k = 3 and 4 fail to display orientationally ordered phases, but that with k = 5 shows isotropic, nematic and, unusually for a hard-particle model, interdigitated smectic A2 phases.</p

Report of the Supersymmetry Theory Working Group

We provide a mini-guide to some of the possible manifestations of weak scale supersymmetry. For each of six scenarios we provide a brief description of the theoretical underpinnings, the adjustable parameters, a qualitative description of the associated phenomenology at future colliders, comments on how to simulate each scenario with existing event generators.Comment: Report of Snowmass Supersymmetry Theory Working Group; 14 pages plus 3 figures using latex2e and snow2e.cls; this version has corrected a number of typos from the first versio