Toward the classification of the realistic free fermionic models

The realistic free fermionic models have had remarkable success in providing plausible explanations for various properties of the Standard Model which include the natural appearance of three generations, the explanation of the heavy top quark mass and the qualitative structure of the fermion mass spectrum in general, the stability of the proton and more. These intriguing achievements makes evident the need to understand the general space of these models. While the number of possibilities is large, general patterns can be extracted. In this paper I present a detailed discussion on the construction of the realistic free fermionic models with the aim of providing some insight into the basic structures and building blocks that enter the construction. The role of free phases in the determination of the phenomenology of the models is discussed in detail. I discuss the connection between the free phases and mirror symmetry in (2,2) models and the corresponding symmetries in the case of the (2,0) models. The importance of the free phases in determining the effective low energy phenomenology is illustrated in several examples. The classification of the models in terms of boundary condition selection rules, real world-sheet fermion pairings, exotic matter states and the hidden sector is discussed.Comment: 43 pages. Standard Late

Spinor-Vector Duality in Heterotic String Orbifolds

The three generation heterotic-string models in the free fermionic formulation are among the most realistic string vacua constructed to date, which motivated their detailed investigation. The classification of free fermion heterotic string vacua has revealed a duality under the exchange of spinor and vector representations of the SO(10) GUT symmetry over the space of models. We demonstrate the existence of the spinor-vector duality using orbifold techniques, and elaborate on the relation of these vacua to free fermionic models.Comment: 20 pages. v2 minor corrections. Version to appear on JHEP. v3 misprints correcte

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

Spectral flow as a map between N=(2,0)-models

The space of $(2,0)$ models is of particular interest among all heterotic-string models because it includes the models with the minimal $SO(10)$ unification structure, which is well motivated by the Standard Model of particle physics data. The fermionic $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic-string models revealed the existence of a new symmetry in the space of string configurations under the exchange of spinors and vectors of the $SO(10)$ GUT group, dubbed spinor-vector duality. Such symmetries are important for the understanding of the landscape of string vacua and ultimately for the possible operation of a dynamical vacuum selection mechanism in string theory. In this paper we generalize this idea to arbitrary internal rational Conformal Field Theories (RCFTs). We explain how the spectral flow operator normally acting within a general $(2,2)$ theory can be used as a map between $(2,0)$ models. We describe the details, give an example and propose more simple currents that can be used in a similar way.Comment: 14 pages, v2: minor changes, added one referenc

M-Theory Model-Building and Proton Stability

We study the problem of baryon stability in M theory, starting from realistic four-dimensional string models constructed using the free-fermion formulation of the weakly-coupled heterotic string. Suitable variants of these models manifest an enhanced custodial gauge symmetry that forbids to all orders the appearance of dangerous dimension-five baryon-decay operators. We exhibit the underlying geometric (bosonic) interpretation of these models, which have a $Z_2 \times Z_2$ orbifold structure similar, but not identical, to the class of Calabi-Yau threefold compactifications of M and F theory investigated by Voisin and Borcea. A related generalization of their work may provide a solution to the problem of proton stability in M theory.Comment: 14 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

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

Non-Abelian Flat Directions in a Minimal Superstring Standard Model

Recently, by studying exact flat directions of non-Abelian singlet fields, we demonstrated the existence of free fermionic heterotic-string models in which the SU(3)_C x SU(2)_L x U(1)_Y-charged matter spectrum, just below the string scale, consists solely of the MSSM spectrum. In this paper we generalize the analysis to include VEVs of non-Abelian fields. We find several, MSSM-producing, exact non-Abelian flat directions, which are the first such examples in the literature. We examine the possibility that hidden sector condensates lift the flat directions.Comment: 14 pages. Standard Late

Towards String Predictions

The aim of superstring phenomenology is to develop the tools and methodology needed to confront string theory with experimental data. The first mandatory task is to find string solutions which reproduce the observable data. The subsequent goal is to extract potential signatures beyond the observable data. Recently, by studying exact flat directions of non-Abelian singlet fields, we demonstrated the existence of free fermionic heterotic-string models in which the $SU(3)\times SU(2)\times U(1)_Y$-charged matter spectrum, just below the string scale, consists solely of the MSSM spectrum. In this paper we study the possibility that the exact flat directions leave a $U(1)_{Z^\prime}$ symmetry unbroken at the Planck scale. We demonstrate in a specific example that such unbroken $U(1)_{Z^\prime}$ is in general expected to be not of the GUT type but of intrinsic stringy origin. We study its phenomenological characteristics and the consequences in the case that $U(1)_{Z^\prime}$ remains unbroken down to low energies. We suggest that observation in forthcoming colliders of a $Z^\prime$, with universal couplings for the two light generations but different couplings for the heavy generation may provide evidence for the $Z_2\times Z_2$ orbifold which underlies the free fermionic models.Comment: 18 pages. Standard Latex. References adde

Physics Implications of Flat Directions in Free Fermionic Superstring Models II: Renormalization Group Analysis

We continue the investigation of the physics implications of a class of flat directions for a prototype quasi-realistic free fermionic string model (CHL5), building upon the results of the previous paper in which the complete mass spectrum and effective trilinear couplings of the observable sector were calculated to all orders in the superpotential. We introduce soft supersymmetry breaking mass parameters into the model, and investigate the gauge symmetry breaking patterns and the renormalization group analysis for two representative flat directions, which leave an additional $U(1)'$ as well as the SM gauge group unbroken at the string scale. We study symmetry breaking patterns that lead to a phenomenologically acceptable $Z-Z'$ hierarchy, $M_{Z^{'}} \sim {\cal O}(1~{\rm TeV})$ and $10^{12}~{\rm GeV}$ for electroweak and intermediate scale $U(1)^{'}$ symmetry breaking, respectively, and the associated mass spectra after electroweak symmetry breaking. The fermion mass spectrum exhibits unrealistic features, including massless exotic fermions, but has an interesting $d$-quark hierarchy and associated CKM matrix in one case. There are (some) non-canonical effective $\mu$ terms, which lead to a non-minimal Higgs sector with more than two Higgs doublets involved in the symmetry breaking, and a rich structure of Higgs particles, charginos, and neutralinos, some of which, however, are massless or ultralight. In the electroweak scale cases the scale of supersymmetry breaking is set by the $Z^{'}$ mass, with the sparticle masses in the several TeV range.Comment: 38 pages, 5 figures, LaTex. Minor correction