John Rizos

A three-generation SU(4)×O(4) string model

Abstract We present a four-dimensional string model whose effective field theory has an O(6)×O(4) gauge symmetry which is broken to the standard model at a very high scale. The fermions of the third generation receive masses from trilinear couplings, retaining the mass relation mb=mt at the GUT scale. All the dangerous color triplets become superheavy while a see-saw mechanism provides the right-handed neutrino with a superheavy mass. The model also predicts a number of “exotic” states with fractional electric charges.

Anomalous U(1)'s in type I string vacua

We perform a systematic string computation of the masses of anomalous U(1) gauge bosons in four-dimensional orientifold vacua, and we study their localization properties in the internal (compactified) space. We find that N = 1 supersymmetric sectors yield four-dimensional contributions, localized in the whole six-dimensional internal space, while N = 2 sectors give contributions localized in four internal dimensions. As a result, the U(1) gauge fields can be much lighter than the string scale, so that when the latter is at the TeV, they can mediate new non-universal repulsive forces at submillimeter distances much stronger than gravity. We also point out that even U(1)s which are free of four-dimensional anomalies may acquire non-zero masses as a consequence of six-dimensional anomalies.

D-branes and the Standard Model

We perform a systematic study of the Standard Model embedding in a D-brane configuration of type I string theory at the TeV scale. We end up with an attractive model and we study several phenomenological questions, such as gauge coupling unification, proton stability, fermion masses and neutrino oscillations. At the string scale, the gauge group is U(3)color×U(2)weak×U(1)1×U(1)bulk. The corresponding gauge bosons are localized on three collections of branes; two of them describe the strong and weak interactions, while the last Abelian factor lives on a brane which is extended in two large extra dimensions with a size of a few microns. The hypercharge is a linear combination of the first three U(1)s. All remaining U(1)s get masses at the TeV scale due to anomalies, leaving the baryon and lepton numbers as (perturbatively) unbroken global symmetries at low energies. The conservation of baryon number assures proton stability, while lepton number symmetry guarantees light neutrino masses that involve a right-handed neutrino in the bulk. The model predicts the value of the weak angle which is compatible with the experiment when the string scale is in the TeV region. It also contains two Higgs doublets that provide tree-level masses to all fermions of the heaviest generation, with calculable Yukawa couplings; one obtains a naturally heavy top and the correct ratio mb/mτ. We also study neutrino masses and mixings in relation to recent solar and atmospheric neutrino data.

N = 1 supersymmetric SU(4) × SU(2)L × SU (2)R effective theory from the weakly coupled heterotic superstring

Abstract In the context of the free-fermionic formulation of the heterotic superstring, we construct a three-generation N = 1 supersymmetric SU(4) × SU(2)L × SU(2)R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in ( 4,2 R ) + ( 4 ,2 R ) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets imposes further restrictions to the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormalizable fermion mass terms up to fifth order shows that in certain string vacua the hierarchy of the fermion families is naturally obtained in the model as the second and third generation fermions earn their mass from fourth- and fifth-order terms. Along certain flat directions it is shown that the ratio of the SU(4) breaking scale and the reduced Planck mass is equal to the up quark ratio m c m t at the string scale. An additional prediction of the model, is the existence of a U(1) symmetry carried by the fields of the hidden sector, ensuring thus the stability of the lightest hidden state. It is proposed that the hidden states may account for the invisible matter of the universe.

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.

Exophobic Quasi-Realistic Heterotic String Vacua

Abstract We demonstrate the existence of heterotic string vacua that are free of massless exotic fields. The need to break the non-Abelian GUT symmetries in k = 1 heterotic string models by Wilson lines, while preserving the GUT embedding of the weak hypercharge and the GUT prediction sin 2 θ w ( M GUT ) = 3 / 8 , necessarily implies that the models contain states with fractional electric charge. Such states are severely restricted by observations, and must be confined or sufficiently massive and diluted. We construct the first quasi-realistic heterotic string models in which the exotic states do not appear in the massless spectrum, and only exist, as they must, in the massive spectrum. The SO ( 10 ) GUT symmetry is broken to the Pati–Salam subgroup. Our PS heterotic string models contain adequate Higgs representations to break the GUT and electroweak symmetry, as well as colour Higgs triplets that can be used for the missing partner mechanism. By statistically sampling the space of Pati–Salam vacua we demonstrate the abundance of quasi-realistic three generation models that are completely free of massless exotics, rendering it plausible that obtaining realistic Yukawa couplings may be possible in this space of models.

Spinor-vector duality in fermionic Z2XZ2 heterotic orbifold models

We continue the classification of the fermionic Z2XZ2 heterotic string vacua with symmetric internal shifts. The space of models is spanned by working with a fixed set of boundary condition basis vectors and by varying the sets of independent Generalized GSO (GGSO) projection coefficients (discrete torsion). This includes the Calabi-Yau like compactifications with (2,2) world-sheet superconformal symmetry, as well as more general vacua with only (2,0) superconformal symmetry. In contrast to our earlier classification that utilized a montecarlo technique to generate random sets of GGSO phases, in this paper we present the results of a complete classification of the subclass of the models in which the four dimensional gauge group arises solely from the null sector. In line with the results of the statistical classification we find a bell shaped distribution that peaks at vanishing net number of generations and with ~15% of the models having three net chiral families. The complete classification reveals a novel spinor-vector duality symmetry over the entire space of vacua. The S V duality interchanges the spinor plus anti-spinor representations with vector representations. We present the data that demonstrates the spinor-vector duality. We illustrate the existence of a duality map in a concrete example. We provide a general algebraic proof for the existence of the S V duality map. We discuss the case of self-dual solutions with an equal number of vectors and spinors, in the presence and absence of E6 gauge symmetry, and present a couple of concrete examples of self-dual models without E6 symmetry.

Classification of Heterotic Pati-Salam Models

Abstract We extend the classification of free fermionic heterotic-string models to vacua in which the SO ( 10 ) GUT symmetry is broken at the string level to the Pati–Salam subgroup. Using our classification method we recently presented the first example of a quasi-realistic heterotic-string vacuum that is free of massless exotic states. Within this method we are able to derive algebraic expressions for the Generalised GSO (GGSO) projections for all sectors that appear in the models. This facilitates the programming of the entire spectrum analysis in a computer code. The total number of vacua in the class of models that we classify is 2 51 ∼ 10 15 . We perform a statistical sampling in this space of models and extract 1011 GGSO configurations with Pati–Salam gauge group. Our results demonstrate that one in every 106 vacua correspond to a three generation exophobic model with the required Higgs states, needed to induce spontaneous breaking to the Standard Model.

The 750 GeV di-photon LHC excess and extra \(Z^\prime \)s in heterotic-string derived models

The ATLAS and CMS collaborations recently recorded possible di-photon excess at 750 GeV and a less significant di-boson excess around 1.9 TeV. Such excesses may be produced in heterotic string derived