Free Fermionic Heterotic String Models Research Articles

A light [formula omitted] heterotic-string derived model

The existence of an extra Z′ inspired from heterotic-string theory at accessible energy scales attracted considerable interest in the particle physics literature. Surprisingly, however, the construction of heterotic-string derived models that allow for an extra Z′ to remain unbroken down to low scales has proven to be very difficult. The main reason being that the U(1) symmetries that are typically discussed in the literature are either anomalous or have to be broken at a high scale to generate light neutrino masses. In this paper we use for that purpose the self-duality property under the spinor vector duality, which was discovered in free fermionic heterotic string models. The chiral massless states in the self-dual models fill complete 27 representations of E6. The anomaly free gauge symmetry in the effective low energy field theory of our string model is SU(4)C×SU(2)L×SU(2)R×U(1)ζ, where U(1)ζ is the family universal U(1) symmetry that descends from E6, and is typically anomalous in other free fermionic heterotic-string models. Our model therefore allows for the existence of a low scale Z′, which is a combination of B−L, U(1)ζ and T3R. The string model is free of exotic fractionally charged states in the massless spectrum. It contains exotic SO(10) singlet states that carry fractional, non-E6 charge, with respect to U(1)ζ. These non-E6 string states arise in the model due to the breaking of the E6 symmetry by discrete Wilson lines. They represent a distinct signature of the string vacua. They may provide viable dark matter candidates.

String Phenomenology: Past, Present and Future Perspectives

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.

SYSTEMATIC INVESTIGATIONS OF THE FREE FERMIONIC HETEROTIC STRING GAUGE GROUP STATISTICS: LAYER 1 RESULTS

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 spacetime 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 [Formula: see text] and [Formula: see text] models are presented.

REDUNDANCIES IN EXPLICITLY CONSTRUCTED TEN-DIMENSIONAL HETEROTIC STRING MODELS

Using Baylor University's C ++ software for construction of weakly coupled free fermionic heterotic string models, called the FF Framework, we explicitly construct the level-1 Kač–Moody ten-dimensional heterotic string models with the aim of understanding the redundancies endemic to this construction method. We show that for models in any even number of large space–time dimensions with a massless left-mover and an odd ordered right-mover, the maximal number of space–time supersymmetries are present. We show that in order to produce all of the models for a given order, different basis vectors must be built; one cannot vary only the GSO coefficients. We also show that all combinations of two order-2 basis vectors do not produce the same models as all possible single order-4 basis vectors, implying the product of the orders used in a search does not necessarily determine the models built. We also show that to build all of the D = 10 level-1 models the inputs must be: sets of single order-6 basis vectors, pairs of basis vectors with orders 3 and 2, or sets of three order-2 basis vectors.

Leptophobic [formula omitted] in heterotic-string derived models

The CDF Collaborationʼs recent observation of an excess of events in the Wjj channel may be attributed to a new Abelian vector boson with suppressed couplings to leptons. While D0 finds no evidence of an excess, the CDF data provide an opportunity to revisit an old result on leptophobic Z′ in heterotic-string derived models. We re-examine the conditions for the existence of a leptophobic U(1) symmetry, which arises from a combination of the U(1)B−L symmetry and the horizontal flavour symmetries, to form a universal U(1) symmetry. While the conditions for the existence of a leptophobic combination are not generic, we show that the left–right symmetric free fermionic heterotic-string models also admit a leptophobic combination. In some cases the leptophobic U(1) is augmented by the enhancement of the colour group, along the lines of models proposed by Foot and Hernandez.

On a NAHE variation

We present a variation of the NAHE-basis for free fermionic heterotic string models. By rotating some of the boundary conditions of the NAHE periodic/anti-periodic fermions { y m , y ¯ m , w m , w ¯ m } , for m = 1 to 6, associated with the six compact dimensions of a bosonic lattice/orbifold model, we show an additional method for enhancing the standard NAHE gauge group of SO ( 10 ) back to E 6 . This rotation transforms ( SO ( 10 ) ⊗ SO ( 6 ) 3 ) obs ⊗ ( E 8 ) hid into ( E 6 ⊗ U ( 1 ) 5 ) obs ⊗ SO ( 22 ) hid . When SO ( 10 ) is enhanced to E 6 in this manner, the ith MSSM matter generation in the SO ( 10 ) 16 i rep, originating in the twisted basis vector b i , recombines with both its associated untwisted MSSM Higgs in a 10 i rep and an untwisted non-Abelian singlet ϕ i , to form a 27 i rep of E 6 . Beginning instead with the E 6 model, the inverse transformation of the fermion boundary conditions corresponds to partial GUT breaking via boundary rotation. Correspondence between free fermionic models with Z 2 ⊗ Z 2 twist (especially of the NAHE class) and orbifold models with a similar twist has received further attention recently. Our NAHE variation also involves a Z 2 ⊗ Z 2 twist and offers additional understanding regarding the free fermion/orbifold correspondence. Further, models based on this NAHE variation offer some different phenomenological features compared to NAHE-based models. In particular, the more compact Z 2 ⊗ Z 2 twist of the NAHE variation offers a range of mirror models not possible from NAHE-based models. Examples of such models are presented.

Classification of heterotic Pati–Salam models

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 10 11 GGSO configurations with Pati–Salam gauge group. Our results demonstrate that one in every 10 6 vacua correspond to a three generation exophobic model with the required Higgs states, needed to induce spontaneous breaking to the Standard Model.

Interpolations among NAHE-based supersymmetric and nonsupersymmetric string vacua

The quasi-realistic free fermionic heterotic-string models provide some of the most detailed examples to explore the phenomenology of string unification. While providing a powerful tool to generate models and their spectra, understanding the realisation of the free fermion models in a bosonic formalism will provide important insight into their basic properties away from the free fermion point. In this Letter we elucidate bosonic equivalent of the basic symmetry breaking pattern in the free fermion models from E8×E8 to SO(16)×SO(16) and exhibit the connection of the free fermion models with corresponding nonsupersymmetric vacua by interpolations.

Searching for extraZ′from strings and other models at the CERN LHC with leptoproduction

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 determinations of the QCD background in this channel, at the tail of the Drell-Yan distributions, in the invariant mass region around $0.8lQl2.5\text{ }\text{ }\mathrm{TeV}$. We focus our analysis primarily on a novel string-inspired ${Z}^{\ensuremath{'}}$, 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 (nonanomalous) ${Z}^{\ensuremath{'}}$ in this kinematic region remains strongly dependent on the size of the new gauge coupling. Weakly coupled extra ${Z}^{\ensuremath{'}}$ will not be easy to identify even with a very good theoretical determination of the QCD background through next-to-next-to-leading order.

SELF-DUALITY AND VACUUM SELECTION

I propose that self-duality in quantum phase-space provides the criteria for the selection of the quantum gravity vacuum. The evidence for this assertion arises from two independent considerations. The first is the phenomenological success of the free fermionic heterotic-string models, which are constructed in the vicinity of the self-dual point under T-duality. The relation between the free fermionic models and the underlying Z2×Z2 toroidal orbifolds is discussed. Recent analysis revealed that the Z2×Z2 free fermionic orbifolds utilize an asymmetric shift in the reduction to three generations, which indicates that the untwisted geometrical moduli are fixed near the self-dual point. The second consideration arises from the recent formulation of quantum mechanics from an equivalence postulate and its relation to phase-space duality. In this context it is demonstrated that the trivial state, with V(q)=E=0, is identified with the self-dual state under phase-space duality. These observations suggest a more general mathematical principle in operation. In physical systems that exhibit a duality structure, the self-dual states under the given duality transformations correspond to critical points.

Nonperturbative flipped SU(5) vacua in heterotic M-theory

The evidence for neutrino masses in atmospheric and solar neutrino experiments provides further support for the embedding of the Standard Model fermions in the chiral 16 SO(10) representation. Such an embedding is afforded by the realistic free fermionic heterotic-string models. In this paper we advance the study of these string models toward a nonperturbative analysis by generalizing the work of Donagi, Pantev, Ovrut and Waldram from the case of G= SU(2 n+1) to G= SU(2 n) stable holomorphic vector bundles on elliptically fibered Calabi–Yau manifolds with fundamental group Z 2 . We demonstrate existence of G= SU(4) solutions with three generations and SO(10) observable gauge group over Hirzebruch base surface, whereas we show that certain classes of del Pezzo base surface do not admit such solutions. The SO(10) symmetry is broken to SU(5)× U(1) by a Wilson line. The overlap with the realistic free fermionic heterotic-string models is discussed.

Flat directions in left-right symmetric string derived models

The only string models known to reproduce the Minimal Supersymmetric Standard Model in the low energy effective field theory are those constructed in the free fermionic formulation. We demonstrate the existence of quasi-realistic free fermionic heterotic-string models in which supersymmetric singlet flat directions do not exist. This raises the possibility that supersymmetry is broken perturbatively in such models by the one-loop Fayet-Iliopoulos term. We show, however, that supersymmetric flat directions that utilize VEVs of some non-Abelian fields in the massless string spectrum do exist in the model. We argue that hidden sector condensates lift the flat directions and break supersymmetry hierarchically.

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) × SU(2) × 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′ symmetry unbroken at the Planck scale. We demonstrate in a specific example that such unbroken U(1) Z′ 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′ remains unbroken down to low energies. We suggest that observation in forthcoming colliders of a Z′, with universal couplings for the two light generations but different couplings for the heavy generation may provide evidence for the Z2 × Z2 orbifold which underlies the free fermionic models.

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× SU (2)L×U(1)Y-charged matter spectrum reduces to that of the MSSM in the effective field theory. In this letter we generalize the analysis to include vevs of non-Abelian fields. We find 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.

D-term spectroscopy in realistic heterotic-string models

The emergence of free fermionic string models with solely the MSSM charged spectrum below the string scale provides further evidence to the assertion that the true string vacuum is connected to the Z_2 x Z_2 orbifold in the vicinity of the free fermionic point in the Narain moduli space. An important property of the Z_2 x Z_2 orbifold is the cyclic permutation symmetry between the three twisted sectors. If preserved in the three generations models the cyclic permutation symmetry results in a family universal anomalous U(1)_A, which is instrumental in explaining squark degeneracy, provided that the dominant component of supersymmetry breaking arises from the U(1)_A D-term. Interestingly, the contribution of the family--universal D_A-term to the squark masses may be intra-family non-universal, and may differ from the usual (universal) boundary conditions assumed in the MSSM. We contemplate how D_A--term spectroscopy may be instrumental in studying superstring models irrespective of our ignorance of the details of supersymmetry breaking. We examine the possible effect of the intra--family non--universality on the resulting SUSY spectrum and the values of the strong coupling, effective weak mixing angle and W-gauge boson mass, up to a two loop accuracy, in the two models (universal and non-universal). We find that non universality relaxes the constraint of color and charge breaking minima which appears in the universal case. In addition, it predicts a 3% smaller value of \alpha_s due to different threshold masses obtained in the latter scenario. Finally, we present the experimentally allowed predictions of the two models in an M_0 and M_{1/2} parameter space.

Intermanual transfer of tactile discrimination

The evidence for neutrino masses in atmospheric and solar neutrino experiments provides further support for the embedding of the Standard Model fermions in the chiral 16 SO(10) representation. Such an embedding is afforded by the realistic free fermionic heterotic-string models. In this paper we advance the study of these string models toward a nonperturbative analysis by generalizing the work of Donagi, Pantev, Ovrut and Waldram from the case of G=SU(2n+1) to G=SU(2n) stable holomorphic vector bundles on elliptically fibered Calabi–Yau manifolds with fundamental group Z2. We demonstrate existence of G=SU(4) solutions with three generations and SO(10) observable gauge group over Hirzebruch base surface, whereas we show that certain classes of del Pezzo base surface do not admit such solutions. The SO(10) symmetry is broken to SU(5)×U(1) by a Wilson line. The overlap with the realistic free fermionic heterotic-string models is discussed.