Free Fermionic String Models Research Articles

Formula omitted

We construct three flipped SU(5)×U(1)X models from F-theory, and consider two such models from free fermionic string model building. To achieve the decoupling scenario in F-theory models and the string-scale gauge coupling unification in free fermionic models, we introduce vector-like particles at the TeV scale that can be observed at the Large Hadron Collider. We study gauge coupling unification, and find that proton decay is within the reach of the future Hyper-Kamiokande experiment. In these models, the doublet–triplet splitting problem and monopole problem can be solved, the neutrino masses and mixings can be explained via the double seesaw or seesaw mechanism, the observed baryon asymmetry can be obtained through leptogenesis, the hybrid inflation can be realized, and the correct cosmic primordial density fluctuations can be generated.

On the number of chiral generations in Z2× Z2 orbifolds

The data from collider experiments and cosmic observatories indicates the existence of three light matter generations. In some classes of string compactifications the number of generations is related to a topological quantity, the Euler characteristic. However, these do not explain the existence of three generations. In a class of free fermionic string models, related to the Z 2× Z 2 orbifold compactification, the existence of three generations is correlated with the existence of three twisted sectors in this class of compactifications. However, the three generation models are constructed in the free fermionic formulation and their geometrical correspondence is not readily available. In this paper we classify quotients of the Z 2× Z 2 orbifold by additional symmetric shifts on the three complex tori. We show that three generation vacua are not obtained in this manner, indicating that the geometrical structures underlying the free fermionic models are more esoteric.

CP violation in realistic string models with family universal anomalous U(1)

The characteristic property of the Z 2× Z 2 orbifold compactification is the cyclic permutation symmetry between the three twisted sectors. We discuss how this property, which is retained in a class of realistic free fermionic string models, may be instrumental in allowing fermion mass hierarchy while ensuring sfermion mass degeneracy, irrespective of the dominant source of supersymmetry breaking. The cyclic symmetry is reflected in some models in the existence of a family universal anomalous U(1) A . We analyze the FCNC and CP violation effects in a model with a dominant U(1) A SUSY breaking. In this theories, new sources of FC are always suppressed with respect to the average sfermion masses. We make a phenomenological analysis of these effects and find that in most of the cases they are in qualitative agreement with the phenomenological limits. The most sensitive low-energy observables to these new FC sources are the ε K parameter, measuring indirect CP violation in neutral kaon mixing and EDMs. These observables set important constraints on the structure of the sfermion mass matrices, but do not require a large fine-tuning of the initial parameters and can be satisfied in most realistic constructions.

Self-interacting dark matter from the hidden heterotic-string sector

It has been suggested recently that self-interacting dark matter (SIDM) fits better the observational characteristics of galaxy dynamics. We propose that the SIDM is composed from the glueballs of the hidden sector non-Abelian gauge group, while the hidden matter states exist in vector-like representation and decouple from the light spectrum. It is shown that these glueballs are semi-stable with the lifetime larger than the present age of the Universe, if their mass is 1 GeV or less. The constraint on their abundance today suggests that the energy was stored in the hidden sector soon after inflation. This imposes an upper limit on the reheating temperature. We further study the naturalness of this scenario in the context of the free-fermionic string models and point out a class of such models where the SIDM from the hidden sector is indeed plausible.

A MINIMAL SUPERSTRING STANDARD MODEL I: FLAT DIRECTIONS

Three family SU (3)C× SU (2)L× 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× SU (2)L× U (1)Y and the SU (3)C× SU (2)L× 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.

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.

Flat directions in three-generation free-fermionic string models

In quasi-realistic string models that contain an anomalous U(1) the non-zero Fayet-Iliopoulos term triggers the shifting of the original vacuum to a new one along some flat direction, so that SUSY is preserved but the gauge group is partially broken. The phenomenological study of these models thus requires as a first step the mapping of the space of flat directions. We investigate F- and D-flat directions in several three-generation SU(3) C × SU(2) L × U(1) Y free-fermionic string models and discuss the typical scenarios that generically arise. When they exist, we systematically construct the flat directions that preserve hypercharge, only break abelian group factors, and can be proven to remain F-flat to all orders in the non-renormalizable superpotential.

Physics implications of flat directions in free fermionic superstring models. I. Mass spectrum and couplings

From the "top-down" approach we investigate physics implications of the class of D- and F- flat directions formed from non-Abelian singlets which are proven flat to all orders in the nonrenormalizable superpotential, for a prototype quasi-realistic free fermionic string model with the standard model gauge group and three families (CHL5). These flat directions have at least an additional U(1)' unbroken at the string scale. For each flat direction, the complete set of effective mass terms and effective trilinear superpotential terms in the observable sector are computed to all orders in the VEV's of the fields in the flat direction. The "string selection-rules" disallow a large number of couplings allowed by gauge invariance, resulting in a massless spectrum with a large number of exotics, in most cases excluded by experiment, thus signifying a generic flaw of these models. Nevertheless, the resulting trilinear couplings of the massless spectrum possess a number of interesting features which we analyse for two representative flat directions: for the fermion texture; baryon- and lepton-number violating couplings; R-parity breaking; non-canonical mu terms; and the possibility of electroweak and intermediate scale symmetry breaking scenarios for U(1)'. The gauge coupling predictions are obtained in the electroweak scale case. Fermion masses possess t-b and tau-mu universality, with the string scale Yukawa couplings g and $g/\sqrt{2}$, respectively. Fermion textures are present for certain flat directions, but only in the down-quark sector. Baryon- and lepton- number violating couplings can trigger proton-decay, $N-{\bar N}$ oscillations, leptoquark interactions and R-parity violation, leading to the absence of a stable LSP.

U(1)′symmetry breaking in supersymmetricE6models

We study the electroweak and $U(1)^{'}$ symmetry breaking patterns in models with the particle content of supersymmetric $E_{6}$, including standard model singlets $S$ and exotic quarks $D,~\bar{D}$. Motivated by free fermionic string models, we do not require $E_{6}$-type relations between Yukawa couplings. In particular, we assume that baryon and lepton numbers are conserved, so that the exotic quarks can be light. Gauge invariance allows Yukawa interactions between $S$ and Higgs doublets, and between $S$ and the exotic quarks, allowing radiative $U(1)^{'}$ symmetry breaking and the generation of an effective $\mu$ parameter at the electroweak scale. For both the $E_{6}$ $\psi$ and $\eta$ models, universal soft supersymmetry breaking parameters and Yukawa universality at the high (string) scale do not yield acceptable low energy phenomenology. Relaxing universality, we find solutions with phenomenologically acceptable values of $M_{Z^{'}}$ and the $Z-Z^{'}$ mixing angle. In addition, by varying the $U(1)^{'}$ charge assignments due to the mixing of $U(1)_{\chi}$ and $U(1)_{\psi}$ of $E_{6}$, it is possible to have acceptable low energy phenomenology with universal boundary conditions.

Asymmetric non-Abelian orbifolds and model building.

The rules for the free fermionic string model construction are extended to include general non-abelian orbifold constructions that go beyond the real fermionic approach. This generalization is also applied to the asymmetric orbifold rules recently introduced. These non-abelian orbifold rules are quite easy to use. Examples are given to illustrate their applications.

STRING NO-SCALE SUPERGRAVITY

We explore the postulates of string no-scale supergravity in the context of free-fermionic string models. The requirements of vanishing vacuum energy, flat directions of the scalar potential, and stable no-scale mechanism impose strong restrictions on possible string no-scale models, which must possess only two or three moduli, and a constrained massless spectrum. The soft-supersymmetry-breaking parameters involving all twisted and untwisted fields are given explicitly. Our calculations take into account the possible existence of an anomalous U A(1) factor in the gauge group, and reveal some novel effects concerning the stability of the no-scale mechanism in the presence of U A(1). This class of models contains no free parameters, i.e. in principle all supersymmetric particle masses and interactions are completely determined. A computerized search for free-fermionic models with the desired properties yields a candidate SU (5)×U(1) model containing extra [Formula: see text] matter representations that allow gauge coupling unification at the string scale. Our candidate model possesses a benign nonuniversal assignment of supersymmetry-breaking scalar masses, which may have interesting low-energy experimental consequences.

Grand unification with three generations in free fermionic string models.

We examine the problem of constructing three generation free fermionic string models with grand unified gauge groups. We attempt the construction of $G\times G$ models, where $G$ is a grand unified group realized at level 1. This structure allows those Higgs representations to appear which are necessary to break the symmetry down to the standard model gauge group. For $G=SO(10)$, we find only models with an even number of generations. However, for $G=SU(5)$ we find a number of 3 generation models.

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.

Supersymmetries in free fermionic strings

Consistent heterotic free fermionic string models are classified in terms of their number of spacetime supersymmetries, N. For each of the six distinct choices of gravitino sector, we determine what number of supersymmetries can survive additional GSO projections. We prove by exhaustive search that only three of the six can yield N = 1, in addition to the N = 4, 2, or 0 that five of the six can yield. One choice of gravitino sector can only produce N = 4 or 0. Relatedly, we find that only Z 2, Z 4, and Z 8 twists of the internal fermions with worldsheet supersymmetry are consistent with N = 1 in free fermionic models. Any other twists obviate N = 1.

Number of generations in free fermionic string models.

In string theory there seems to be an intimate connection between spacetime and world-sheet physics. Following this line of thought we investigate the family problem in a particular class of string solutions, namely the free fermionic string models. We find that the number of generations $N_g$ is related to the index of the supersymmetry generator of the underlying $N=2$ internal superconformal field theory which is always present in any $N=1$ spacetime supersymmetric string vacuum. We also derive a formula for the index and thus for the number of generations which is sensitive to the boundary condition assignments of the internal fermions and to certain coefficients which determine the weight with which each spin-structure of the model contributes to the one-loop partition function. Finally we apply our formula to several realistic string models in order to derive $N_g$ and we verify our results by constructing explicitly the massless spectrum of these string models.

Threshold effects in grand unified string models

A common feature in most of the string derived models is the appearance of extra matter fields, beyond those needed for the standard model content, which usually become massive at various intermediate scales. In the present work we concentrate on the free fermionic string models based on the intermediate gauge symmetries SU(5) × U(1) and SU(4) × O(4) and investigate the effect on the low energy parameters due to the inclusion of threshold corrections introduced either by string massive states or states becoming massive close to the intermediate symmetry breaking scale.

Gauge and matter condensates in realistic string models

We examine the inter-relationship of the superpotential containing hidden and observable matter fields and the ensuing condensates in free fermionic string models. These gauge and matter condensates of the strongly interacting hidden gauge groups play a crucial role in the determination of the physical parameters of the observable sector. Supplementing the above information with the requirement of modular invariance, we find that a generic model with only trilinear superpotential allows for a degenerate (and sometimes pathological) set of vacua. This degeneracy may be lifted by higher order terms in the superpotential. We also point out some other subtle points than may arise in calculations of this nature. We exemplify our observations by computing explicitly the modular invariant gaugino and matter condensates in the flipped SU(5) string model with hidden gauge group SO(10)×SU(4).