String derived MSSM and M-theory unification

Physical Review D, 2005

String theories in principle address the origin and values of the quark and lepton masses. Perhaps the small values of neutrino masses could be explained generically in string theory even if it is more difficult to calculate individual values, or perhaps some string constructions could be favored by generating small neutrino masses. We examine this issue in the context of the well-known threefamily standard-like Z3 heterotic orbifolds, where the theory is well enough known to construct the corresponding operators allowed by string selection rules, and analyze the D-and F-flatness conditions. Surprisingly, we find that a simple see-saw mechanism does not arise. It is not clear whether this is a property of this construction, or of orbifolds more generally, or of string theory itself. Extended see-saw mechanisms may be allowed; more analysis will be needed to settle that issue. We briefly speculate on their form if allowed and on the possibility of alternatives, such as small Dirac masses and triplet see-saws. The smallness of neutrino masses may be a powerful probe of string constructions in general. We also find further evidence that there are only 20 inequivalent models in this class, which affects the counting of string vacua.

The European Physical Journal C, 2008

The Standard Model indicates the realization of grand unified structures in nature, and can only be viewed as an effective theory below a higher energy cutoff. While the renormalizable Standard Model forbids proton decay mediating operators due to accidental global symmetries, many extensions of the Standard Model introduce such dimension four, five and six operators. Furthermore, quantum gravity effects are expected to induce proton instability, indicating that the higher energy cutoff scale must be above 10 16 GeV. Quasirealistic heterotic string models provide the arena to explore how perturbative quantum gravity affects the particle physics phenomenology. An appealing explanation for the proton longevity is provided by the existence of an Abelian gauge symmetry that suppresses the proton decay mediating operators. Additionally, such a low-scale U (1) symmetry should: allow the suppression of the left-handed neutrino masses by a seesaw mechanism; allow fermion Yukawa couplings to the electroweak Higgs doublets; be anomaly free; be family universal. These requirements render the existence of such U (1) symmetries in quasi-realistic heterotic string models highly non-trivial. We demonstrate the existence of a U (1) symmetry that satisfies all of the above requirements in a class of left-right symmetric heterotic string models in the free fermionic formulation. The existence of the extra Z ′ in the energy range accessible to future experiments is motivated by the requirement of adequate suppression of proton decay mediation. We further show that while the extra U (1) forbids dimension four baryon number violating operators it allows dimension four lepton number violating operators and R-parity violation.

Physical Review D, 2008

Discovery potentials for extra neutral interactions at the Large Hadron Collider in forthcoming experiments are analyzed using resonant leptoproduction. For this purpose we use high precision next-to-next-to-leading order (NNLO) determinations of the QCD background in this channel, at the tail of the Drell-Yan distributions, in the invariant mass region around 0.8 < Q < 2.5 TeV. We focus our analysis primarily on a novel string-inspired Z ′ , obtained in left-right symmetric free fermionic heterotic string models and whose existence at low energies is motivated by its role in suppressing proton decay mediation. We analyze the parametric dependence of the predictions and perform comparison with other models based on bottom up approaches, that are constructed by requiring anomaly cancellation and enlarged Higgs structure. We show that the results are not particularly sensitive to the specific charge assignments. This may render quite difficult the extraction of significant information from the forward-backward asymmetries on the resonance, assuming that these are possible due to a sizeable width. The challenge to discover extra (non anomalous) Z ′ in this kinematic region remains strongly dependent on the size of the new gauge coupling. Weakly coupled extra Z ′ will not be easy to identify even with a very good theoretical determination of the QCD background through NNLO.

Modern Physics Letters A, 2011

Using software under development at Baylor University, we explicitly construct all layer 1 gauge, weakly coupled free fermionic heterotic string models up to order 22 in four large space-time dimensions. The gauge models consist primarily of gauge content making a systematic construction process efficient. We present an overview of the model building procedure, redundancies in the process, methods used to reduce such redundancies and statistics regarding the occurrence of various combinations of gauge group factors and GUT groups. Statistics for both N = 4 and N = 0 models are presented.

The European Physical Journal C, 2016

Physical Review D, 2007

For the weakly coupled heterotic string (WCHS) there is a well-known factor of twenty conflict between the minimum string coupling unification scale, Λ H ∼ 5 × 10 17 GeV, and the projected MSSM gauge coupling unification scale, Λ U ∼ 2.5×10 16 GeV, assuming an intermediate scale desert (ISD). From a bottom-up approach, renormalization effects of intermediate scale MSSM-charged exotics (ISME), which are endemic to quasi-realistic string models, can resolve this issue by pushing the MSSM scale up to the string scale. However, for a generic string model, this implies that the projected Λ U unification under the ISD assumption is accidental.

Physical Review D, 2013

We explore the phenomenological viability of a light Z ′ in heterotic-string models, whose existence has been motivated by proton stability arguments. A class of quasi-realistic string models that produce such a viable Z ′ are the Left-Right Symmetric (LRS) heterotic-string models in the free fermionic formulation. A key feature of these models is that the matter charges under U (1) Z ′ do not admit an E 6 embedding. The light Z ′ in the LRS heteroticstring models forbids baryon number violating operators, while allowing lepton number violating operators, hence suppressing proton decay yet allowing for sufficiently small neutrino masses via a seesaw mechanism. We show that the constraints imposed by the gauge coupling data and heterotic-string coupling unification nullify the viability of a light Z ′ in these models. We further argue that agreement with the gauge coupling data necessitates that the U (1) Z ′ charges admit an E 6 embedding. We discuss how viable string models with this property may be constructed.

Galaxies, 2014

The observation of a scalar resonance at the Large Hadron Collider (LHC), compatible with perturbative electroweak symmetry breaking, reinforces the Standard Model (SM) parameterisation of all subatomic data. The logarithmic evolution of the SM gauge and matter parameters suggests that this parameterisation remains viable up to the Planck scale, where gravitational effects are of comparable strength. String theory provides a perturbatively consistent scheme to explore how the parameters of the Standard Model may be determined from a theory of quantum gravity. The free fermionic heterotic string models provide concrete examples of exact string solutions that reproduce the spectrum of the Minimal Supersymmetric Standard Model. Contemporary studies entail the development of methods to classify large classes of models. This led to the discovery of exophobic heterotic-string vacua and the observation of spinor-vector duality, which provides an insight to the global structure of the space of (2,0) heterotic-string vacua. Future directions entail the study of the role of the massive string states in these models and their incorporation in cosmological scenarios. A complementary direction is the formulation of quantum gravity from the principle of manifest phase space duality and the equivalence postulate of quantum mechanics, which suggest that space is compact. The compactness of space, which implies intrinsic regularisation, may be tightly related to the intrinsic finite length scale, implied by string phenomenology.

Nuclear Physics B, 2002

Grand unification and its incarnation in the form of heterotic-string unification, are the only extensions of the Standard Model that are rooted in the structure of the Standard Model itself. In this context it was proposed that the exclusiveness of proton stability and suppression of neutrino masses necessitates the existence of an additional U (1) Z ′ symmetry, which is of non-GUT origin and remains unbroken down to intermediate or low energies. Realistic string models frequently give rise to non-GUT U (1) symmetries, which arise from the flavor symmetries in the models. In this paper we demonstrate in a string-inspired toy model that such a stringy Z ′ can indeed guarantee proton longevity and viable phenomenology in the neutrino sector as well as in the quark and charged lepton sectors.

The European Physical Journal C, 2019

I argue that the ten dimensional non-supersymmetric tachyonic superstrings may serve as good starting points for the construction of viable phenomenological vacua. Thus, enlarging the space of possible solutions that may address some of the outstanding problems in string phenomenology. A tachyon free six generation Standard-like Model is presented, which can be regarded as an orbifold of the SO(16) × E 8 heterotic-string in ten dimensions. I propose that any (2, 0) heterotic-string in four dimensions can be connected to a (2, 2) one via an orbifold or by interpolations and provide some evidence for this conjecture. It suggests that any Effective Field Theory (EFT) model that cannot be connected to a (2, 2) theory is necessarily in the swampland, and will simplify the analysis of the moduli spaces of (2, 0) string compactifications.

Physical Review D, 2010

In this paper, we discuss the issues of supersymmetry breaking and moduli stabilization within the context of E 8 E 8 heterotic orbifold constructions and, in particular, we focus on the class of ''minilandscape'' models. In the supersymmetric limit, these models admit an effective low-energy field theory with a spectrum of states and dimensionless gauge and Yukawa couplings very much like that of the minimal supersymmetric standard model. These theories contain a non-Abelian hidden gauge sector which generates a nonperturbative superpotential leading to supersymmetry breaking and moduli stabilization. We demonstrate this effect in a simple model which contains many of the features of the more general construction. In addition, we argue that once supersymmetry is broken in a restricted sector of the theory, then all moduli are stabilized by supergravity effects. Finally, we obtain the low-energy superparticle spectrum resulting from this simple model.

Reports on Progress in Physics, 2011

The Standard Model is the theory describing all observational data from the highest energies to the largest distances. [There is however one caveat; additional forms of energy, not part of the Standard Model, known as dark matter and dark energy must be included in order to describe the universe at galactic scales and larger.] High energies refers to physics at the highest energy particle accelerators, including CERN's LEP II (which ceased operation in 2000 to begin construction of the LHC or Large Hadron Collider now operating) and Fermilab's Tevatron, as well as to the energies obtained in particle jets created in so-called active gallactic nuclei scattered throughout the visible universe. Some of these extra-galactic particles bombard our own earth in the form of cosmic rays, or super-energetic protons which scatter off nucei in the upper atmosphere. String theory is, on the other hand, an unfinished theoretical construct which attempts to describe all matter and their interactions in terms of the harmonic oscillations of open and/or closed strings. It is regarded as unfinished since at the present it is a collection of ideas, tied together by powerful consistency conditions, called dualities, with the ultimate goal of finding the completed String Theory. At the moment we only have descriptions which are valid in different mutually exclusive limits with names like, Type I, IIA, IIB, heterotic, M and F theory. The string landscape has been described in the pages of many scholarly and popular works. It is perhaps best understood as the collection of possible solutions to the string equations. Albeit these solutions look totally different in the different limiting descriptions. What do we know about the String Landscape? We know that there are such a large number of possible solutions that the only way to represent this number is as 10 500 or a one followed by 500 zeros. Note this isn't a precise value since the uncertainty is given by a number just as large. Moreover, we know that most of these string states look nothing like the Standard Model. They have the wrong matter and wrong forces. Moreover they are not off by a small amount, they are totally wrong. So the question becomes, does string theory really describe our observable world? In order to address this question, one must find at least one string state that resembles it. One possibility is that our observable world is in fact a unique string state. If this is the case, then the problem becomes one of finding the proverbial needle in the largest possible haystack! On the other hand, there may be many states which are sufficiently close to the observable world, and we need only to understand why we are in this finite subspace of the string landscape. And perhaps there are good reasons, why this subspace is preferred over 99.999999999...% of the myriad of non-Standard-Model-like string states. Perhaps, just by confining our attention to this subspace we can learn something about our observable world which we can not learn otherwise. Thus the

Journal of High Energy Physics, 2007

We construct a supersymmetric standard model in the context of the Z 12−I orbifold compactification of the heterotic string theory. The gauge group is SU(3) c × SU(2) L × U(1) Y × U(1) 4 × [SO(10) × U(1) 3 ] ′. We obtain three chiral families, 3 × {Q, d c , u c , L, e c , ν c }, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of sin 2 θ 0 W = 3 8 and another exactly massless exphoton (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, α and α, SU(2) L doublet exotics, δ and δ, and SU(3) c × SU(2) L singlet but Y = 2 3 , − 1 3 , − 2 3 , 1 3 exotics, ξ, η, ξ, η. We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but sin 2 θ 0 W = 3 14 .

Journal of High Energy Physics, 2002

In four dimensional superstring models, the gauge group normally contains extra U (1)s that are broken at a high energy scale. We show that the presence of the extra U (1)s is crucial for the phenomenological viability of string scenarios, since the contribution to the scalar masses from the D-terms can lift the unbounded from below directions that usually appear when the gauge group at high energies is just the Standard Model group. In particular, we show that the dilaton dominated scenario can be allowed in large regions of the parameter space if there exists an anomalous U (1) in the theory, and the charges of the particles are the appropriate ones. We also analyze the parameter space of some explicit string constructions, imposing a correct phenomenology and the absence of dangerous charge and color breaking minima or unbounded from below directions.

Physical Review D, 2015

The free fermionic construction of the heterotic string in four dimensions produced a large space of three generation models with the underlying SO(10) embedding of the Standard Model states. The SO(10) symmetry is broken to a subgroup directly at the string scale. Over the past few years free fermionic models with the Pati-Salam and flipped SU (5) subgroups have been classified. In this paper we extend this classification program to models in which the SO(10) symmetry is broken at the string level to the SU (4) × SU (2) L × U (1) R (SU421) subgroup. The subspace of free fermionic models that we consider corresponds to symmetric Z 2 × Z 2 orbifolds. We provide a general argument that shows that this class of SU421 free fermionic models cannot produce viable three generation models.

The European Physical Journal C, 2016

A di-photon excess at the LHC can be explained as a Standard Model singlet that is produced and decays by heavy vector-like colour triplets and electroweak doublets in one-loop diagrams. The characteristics of the required spectrum are well motivated in heterotic-string constructions that allow for a light Z . Anomaly cancellation of the U (1) Z symmetry requires the existence of the Standard Model singlet and vector-like states in the vicinity of the U (1) Z breaking scale. In this paper we show that the agreement with the gauge coupling data at one-loop is identical to the case of the Minimal Supersymmetric Standard Model, owing to cancellations between the additional states. We further show that effects arising from heavy thresholds may push the supersymmetric spectrum beyond the reach of the LHC, while maintaining the agreement with the gauge coupling data. We show that the string-inspired model can indeed produce an observable signal and discuss the feasibility of obtaining viable scalar mass spectrum.