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Register a new userNon-Tachyonic Semi-Realistic Non-Supersymmetric Heterotic String Vacua
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The heterotic--string models in the free fermionic formulation gave rise to some of the most realistic string models to date, which possess N=1 spacetime supersymmetry. Lack of evidence for supersymmetry at the LHC instigated recent interest in non-supersymmetric heterotic-string vacua. We explore what may be learned in this context from the quasi--realistic free fermionic models. We show that constructions with a low number of families give rise to proliferation of a priori tachyon producing sectors, compared to the non--realistic examples, which typically may contain only one such sector. The reason being that in the realistic cases the internal six dimensional space is fragmented into smaller units. We present one example of a quasi--realistic, non--supersymmetric, non--tachyonic, heterotic--string vacuum and compare the structure of its massless spectrum to the corresponding supersymmetric vacuum. While in some sectors supersymmetry is broken explicitly, i.e. the bosonic and fermionic sectors produce massless and massive states, other sectors, and in particular those leading to the chiral families, continue to exhibit fermi-bose degeneracy. In these sectors the massless spectrum, as compared to the supersymmetric cases, will only differ in some local or global U(1) charges. We discuss the conditions for obtaining $n_b=n_f$ at the massless level in these models. Our example model contains an anomalous U(1) symmetry, which generates a tadpole diagram at one loop-order in string perturbation theory. We speculate that this tadpole diagram may cancel the corresponding diagram generated by the one-loop non-vanishing vacuum energy and that in this respect the supersymmetric and non-supersymmetric vacua should be regarded on equal footing. Finally we discuss vacua that contain two supersymmetry generating sectors.
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We extend the classification of fermionic $mathbb{Z}_2timesmathbb{Z}_2$ heterotic string orbifolds to non--supersymmetric Pati--Salam (PS) models in two classes of vacua, that we dub $tilde S$--models and $S$--models. The first correspond to compactifications of a tachyonic ten--dimensional vacuum, whereas the second correspond to compactifications of the ten--dimensional tachyon--free $SO(16)times SO(16)$ heterotic string. In both cases we develop a systematic method to extract tachyon--free four--dimensional models. We show that tachyon--free configurations arise with probability $sim0.002$ and $sim0.01$ in the first and second case, respectively. We adapt the `fertility methodology that facilitates the extraction of phenomenological models. We show that Pati--Salam $tilde S$--models do not contain heavy Higgs scalar representations that are required to break the PS symmetry to the Standard Model and are therefore not phenomenologically viable. Hence, we argue that in $tilde S$--models the $SO(10)$ GUT symmetry must be broken at the string scale to the Standard--like Model subgroup. We extract tachyon--free three generation models in both cases that contain an equal number of massless bosonic and fermionic degrees of freedom, ${it i.e.}$ with $a_{00}=N_b^0-N_f^0=0$, and analyse their one--loop partition function.
Recently it was proposed that ten-dimensional tachyonic string vacua may serve as starting points for the construction of viable four dimensional phenomenological string models which are tachyon free. This is achieved by projecting out the tachyons in the four-dimensional models using projectors other than the projector which is utilised in the supersymmetric models and those of the $SO(16)times SO(16)$ heterotic string. We continue the exploration of this class of models by developing systematic computerised tools for their classification, the analysis of their tachyonic and massless spectra, as well as analysis of their partition functions and vacuum energy. We explore a randomly generated space of $2times10^9$ string vacua in this class and find that tachyon--free models occur with $sim 5times 10^{-3}$ probability, and of those, phenomenologically inclined $SO(10)$ vacua with $a_{00}=N_b^0-N_f^0=0$, i.e. equal number of fermionic and bosonic massless states, occur with frequency $sim 2times 10^{-6}$. Extracting larger numbers of phenomenological vacua therefore requires adaptation of fertility conditions that we discuss, and significantly increase the frequency of tachyon--free models. Our results suggest that spacetime supersymmetry may not be a necessary ingredient in phenomenological string models, even at the Planck scale.
In global supersymmetric Wess-Zumino models with minimal Kahler potentials, F-type supersymmetry breaking always yields instability or continuous degeneracy of non-supersymmetric vacua. As a generalization of the original ORaifeartaighs result, the existence of instability or degeneracy is true to any higher order corrections at tree level for models even with non-renormalizable superpotentials. The degeneracy generically coincides the R-axion direction under some assumptions of R-charge assignment, but generally requires neither R-symmetries nor any assumption of generic superpotentials. The result also confirms the well-known fact that tree level supersymmetry breaking is a very rare occurrence in global supersymmetric theories with minimal Kahler potentials. The implication for effective field theory method in the landscape is discussed and we point out that choosing models with minimal Kahler potentials may result in unexpected answers to the vacuum statistics. Supergravity theories or theories with non-minimal Kahler potentials in general do not suffer from the existence of instability or degeneracy. But very strong gauge dynamics or small compactification dimension reduces the Kahler potential from non-minimal to minimal, and gravity decoupling limit reduces supergravity to global supersymmetry. Instability or degeneracy may appear in these limits. Away from these limits, a large number of non-SUSY vacua may still be found in an intermediate region.
Leptoquarks extending the Standard Model (SM) are attracting an increasing attention in the recent literature. Hence, the identification of 4D SM-like models and the classification of allowed leptoquarks from strings is an important step in the study of string phenomenology. We perform the most extensive search for SM-like models from the non-supersymmetric heterotic string $mathrm{SO}(16)timesmathrm{SO}(16)$, resulting in more than 170,000 inequivalent promising string models from 138 Abelian toroidal orbifolds. We explore the 4D massless particle spectra of these models in order to identify all exotics beside the three generations of quarks and leptons. Hereby, we learn which leptoquark can be realized in this string setup. Moreover, we analyze the number of SM Higgs doublets which is generically larger than one. Then, we identify SM-like models with a minimal particle content. These so-called almost SM models appear most frequently in the orbifold geometries $mathbb Z_2timesmathbb Z_4$ (2,4) and (1,6). Finally, we apply machine learning to our dataset in order to predict the orbifold geometry where a given particle spectrum can be found most likely.
Classification of Left-Right Symmetric (LRS) heterotic-string vacua in the free fermionic formulation, using random generation of generalised GSO (GGSO) projection coefficients, produced phenomenologically viable models with probability $4times 10^{-11}$. Extracting substantial number of phenomenologically viable models requires modification of the classification method. This is achieved by identifying phenomenologically amenable conditions on the Generalised GSO projection coefficients that are randomly generated at the $SO(10)$ level. Around each of these fertile cores we perform a complete LRS classification, generating viable models with probabilility $1.4times 10^{-2}$, hence increasing the probability of generating phenomenologically viable models by nine orders of magnitude, and producing some $1.4times 10^5$ such models. In the process we identify a doublet-triplet selection mechanism that operates in twisted sectors of the string models that break the $SO(10)$ symmetry to the Pati-Salam subgroup. This mechanism therefore operates as well in free fermionic models with Pati-Salam and Standard-like Model $SO(10)$ subgroups.
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