Alon E. Faraggi

The vacuum structure and spectrum of N=2 supersymmetric SU(n) gauge theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional {ital N}=2 supersymmetric SU({ital n}) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus {ital n}{minus}1 hyperelliptic Riemann surfaces.

A new standard-like model in the four dimensional free fermionic string formulation

Abstract I present a new three generation superstring standard-like model in the free fermionic formulation with the following properties. The complete massless spectrum is derived and shown to be anomaly free apart from a single anomalous U(1). The Dine-Seiberg-Witten mechanism is applied to cancel the anomaly, leaving a supersymmetric vacuum. I show that the resulting observable gauge symmetry is SU(3)×SU(2)×U(1) n where n = 1 or 2. All trilinear superpotential couplings have been calculated. I show that of the standard model quarks and leptons only +2 3 charged quarks obtain a non vanishing trilevel coupling, which suggest a possible explanation for the heaviness of the top quark relative to the lighter quarks and leptons. The additional, generation independent, U(1) symmetry may remain unbroken down to low energies and prevents fast proton decay.

A standard-like model in the four-dimensional free fermionic string formulation

Abstract We show how the Standard Model may be derived from the heterotic string with no intermediate energy scale by using the free fermionic formulation. An explicit model is presented, with the following properties: (i) The observable gauge group is SU(3)C × SU(2)L × U(1)n where n = 1 or 2, after a possible symmetry breaking at the string level. (ii) The complete massless spectrum is derived and is shown to be anomaly free apart from a single “anomalous” U(1). In the observable sector there are only three generations of chiral fermions with their superpartners. (iii) There are enough scalar doublets and singlets to break the gauge symmetry in a realistic way. (iv) All trilinear superpotential couplings have been calculated. (v) The weak hypercharge is uniquely defined, including a possible new, generation independent, U(1) symmetry, which may remain unbroken down to low energies, and prevents fast proton decay.

Construction of realistic standard-like models in the free fermionic superstring formulation

Abstract I discuss in detail the construction of realistic superstring standard-like models in the four dimensional free fermionic formulation. The analysis results in a restricted class of models with unique characteristics: (i) Three and only three generations of chiral fermions with their superpartners and the correct standard model quantum numbers. (ii) Proton decay from dimension four and dimension five operators is suppressed due to gauged U(1) symmetries. (iii) There exist Higgs doublets from two distinct sectors, which can generate realistic symmetry breaking. (iv) These models explain the top-bottom mass hierarchy. At the trilinear level of the superpotential only the top quark gets a nonvanishing mass term. The bottom quark and the lighter quarks and leptons get their mass terms from nonrenormalizable terms. This result is correlated with the requirement of a supersymmetric vacuum at the Planck scale. (v) The models predict the existence of small hidden gauge groups, like SU(3), with matter spectrum in vector representations.

String Derived MSSM and M-theory Unification

Abstract The recent conjecture of possible equivalence between the string scale M S and the minimal supersymmetric standard model unification scale M U ≈2.5×10 16 GeV is considered in the context of string models. This conjecture suggests that the observable gauge group just below the string scale should be SU (3) C × SU (2) L × U (1) Y and that the SU (3) C × SU (2) L × U (1) Y -charged spectrum of the observable sector should consist solely of the MSSM spectrum. We demonstrate that string models can actually be constructed that possess these observable features. Two aspects generic to many classes of three family SU (3) C × SU (2) L × U (1) Y string models are both an extra local anomalous U (1) A and numerous (often fractionally charged) exotic particles beyond the MSSM. Thus, for these classes, the key to obtaining an M S = M U ≈2.5×10 16 GeV string model is the existence of F - and D -flat directions that near the string scale can simultaneously break the anomalous U (1) and give mass to all exotic SM-charged observable particles, decoupling them from the low energy spectrum. In this letter we show, in the context of free fermionic strings, that string models with flat directions possessing these features do exist. We present one such string derived model in which all such exotic observable states beyond the MSSM receive mass at the scale generated by the Fayet–Iliopoulos term. The associated F - and D -flat direction is proven flat to all orders of the superpotential.

Hierarchical top - bottom mass relation in a superstring derived standard - like model

Abstract I propose a mechanism in a class of superstring standard-like models which explains the mass hierarchy between the top and bottom quarks. At the trilinear level of the superpotential only the top quark gets a nonvanishing mass term while the bottom quarks and tau lepton mass terms are obtained from nonrenormalizable terms. I construct a model which realized this mechanism. In this model the bottom quark and tau lepton Yukawa couplings are obtained from quartic order terms. I show that λ b = λ τ ≈ 1 8 λ t at the unification scale. A naive estimate yields mt∼175−180 GeV.

Z2×Z2 orbifold compactification as the origin of realistic free fermionic models

I discuss the correspondence between realistic four dimensional free fermionic models and Z2×Z2 orbifold compactification. I discuss the properties of the Z2×Z2 orbifold that are reflected in the realistic free fermionic models. I argue that the properties zof the realistic free fermionic models arise due to the underlying Z2×Z2 orbifold compactification with nontrivial background fields. I suggest that three generations is a natural outcome of Z2×Z2 orbifold compactification with “standard embedding” and at the point in compactification space that corresponds to the free fermionic formulation. I discuss how quark flavor mixing is related to the compactification.

Gauge coupling unification in realistic free-fermionic string models

We discuss the unification of gauge couplings within the framework of a wide class of realistic free-fermionic string models which have appeared in the literature, including the flipped SU(5), SO(6) × SO(4), and various SU(3) × SU(2) × U(1) models. If the matter spectrum below the string scale is that of the Minimal Supersymmetric Standard Model (MSSM), then string unification is in disagreement with experiment. We therefore examine several effects that may modify the minimal string predictions. First, we develop a systematic procedure for evaluating the one-loop heavy string threshold corrections in free-fermionic string models, and we explicitly evaluate these corrections for each of the realistic models. We find that these string threshold corrections are small, and we provide general arguments explaining why such threshold corrections are suppressed in string theory. Thus heavy thresholds cannot resolve the disagreement with experiment. We also study the effect of non-standard hypercharge normalizations, light SUSY thresholds, and intermediate-scale gauge structure, and similarly conclude that these effects cannot resolve the disagreement with low-energy data. Finally, we examine the effects of additional color triplets and electroweak doublets beyond the MSSM. Although not required in ordinary grand unification scenarios, such states generically appear within the context of certain realistic free-fermionic string models. We show that if these states exist at the appropriate thresholds, then the gauge couplings will indeed unify at the string scale. Thus, within these string models, string unification can be in agreement with low-energy data.

Generation mass hierarchy in superstring derived models

I discuss the problem of generation mass hierarchy in the context of realistic superstring models which are constructed in the free fermionic formulation. These models correspond to models which are compactified on a Z2 × Z2 orbifold. I suggest that the hierarchy among the generations results from horizontal symmetries, which arise from the compactification. In particular, I show that in a class of free fermionic standard-like models, the suppression of the mass terms for the hightest generation is a general, and unambiguous, characteristic of these models. I show that the mixing between the generations is suppressed due to the horizontal symmetries. I conclude that these models may potentially explain the generation mass hierarchy.

Chiral family classification of fermionic Z2xZ2 heterotic orbifold models

Free fermionic construction of four dimensional string vacua, are related to the Z2XZ2 orbifolds at special points in the moduli space, and yielded the most realistic three family string models to date. Using free fermionic construction techniques we are able to classify more than 10^10 string vacua by the net family and anti-family number. Using a montecarlo technique we find that a bell shaped distribution that peaks at vanishing net number of chiral families. We also observe that ~15% of the models have three net chiral families. We find that in addition to mirror symmetry that the distribution exhibits a symmetry under the exchange of (spinor plus anti-spinor) representations with vectorial representations.