Heterotic String Models Research Articles

Interpolation and exponentially suppressed cosmological constant in non-supersymmetric heterotic strings with general [formula omitted] twists

We study general non-supersymmetric heterotic string models, including so-called interpolating models, d-dimensionally compactified with the arbitrary number of freely acting Z2 twisted directions. Taking the limits of the compactified radii to zero and infinity (the endpoint limits), we show some examples of the various interpolation patterns in the d=2 (8-dimensional) case. In the region where supersymmetry is asymptotically restored, we derive the formula for the one-loop cosmological constant of (10−d) dimensional non-supersymmetric heterotic string models with general Z2 twists, which does not depend on all the other endpoints and find out the points in the moduli space where the cosmological constant is exponentially suppressed. The moduli stability of the cosmological constant is also analyzed.

Heterotic String Model Building with Monad Bundles and Reinforcement Learning

AbstractWe use reinforcement learning as a means of constructing string compactifications with prescribed properties. Specifically, we study heteroticGUT models on Calabi‐Yau three‐folds with monad bundles, in search of phenomenologically promising examples. Due to the vast number of bundles and the sparseness of viable choices, methods based on systematic scanning are not suitable for this class of models. By focusing on two specific manifolds with Picard numbers two and three, we show that reinforcement learning can be used successfully to explore monad bundles. Training can be accomplished with minimal computing resources and leads to highly efficient policy networks. They produce phenomenologically promising states for nearly 100% of episodes and within a small number of steps. In this way, hundreds of new candidate standard models are found.

Satisfiability modulo theories and chiral heterotic string vacua with positive cosmological constant

We apply Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers in the context of finding chiral heterotic string models with positive cosmological constant from Z2×Z2 orbifolds. The power of using SAT/SMT solvers to sift large parameter spaces quickly to decide satisfiability, both to declare and prove unsatisfiability and to declare satisfiability, are demonstrated in this setting. These models are partly chosen to be small enough to plot the performance against exhaustive search, which takes around 2 hours 20 minutes to comb through the parameter space. We show that making use of SMT based techniques with integer encoding is rather simple and effective, while a more careful Boolean SAT encoding provides a significant speed-up – determining satisfiability or unsatisfiability has, in our experiments varied between 0.03 and 0.06 seconds, while determining all models (where models exist) took 19 seconds for a constraint system that allows for 2048 models and 8.4 seconds for a constraint system that admits 640 models. We thus gain several orders of magnitude in speed, and this advantage is set to grow with a growing parameter space. This holds the promise that the method scales well beyond the initial problem we have used it for in this paper.

Spinor–vector duality and sterile neutrinos in string derived models

The MiniBooNE collaboration found evidence for the existence of sterile neutrinos, at a mass scale comparable to the active left–handed neutrinos. While sterile neutrinos arise naturally in large volume string scenarios, they are more difficult to accommodate in heterotic–string derived models that reproduce the GUT embedding of the Standard Model particles. Sterile neutrinos in heterotic–string models imply the existence of an additional Abelian gauge symmetry at low scales, possibly within reach of contemporary colliders. I discuss the construction of string derived Z′ models that utilise the spinor–vector duality to guarantee that the extra U(1) Z′ symmetry can remain unbroken down to low scales.

U(1)′ coupling constant at low energies from heterotic orbifolds

Additional Abelian gauge interactions are generic to string compactifications. In heterotic string models, gauge coupling unification of such forces and other gauge interactions is natural due to their common origin. In this letter we study systematically the 1-loop running of the coupling constants in effective vacua emerging from Z8 heterotic orbifold compactifications that provide the matter spectrum of the MSSM plus some vectorlike exotics, restricting to vacua that yield a non-anomalous U(1)′ symmetry, gauge coupling unification and the observed values of known gauge couplings. We determine the low-energy value of the U(1)′ coupling constant for different scales of supersymmetry breakdown. We find that the U(1)′ coupling constant is quite restricted in string models to lie in the range 0.46–0.7 for low-scale supersymmetry or 0.44–0.6 in other cases. We argue that the phenomenology of these string vacua should be further explored to solve some extant issues, such as the stability of the Higgs vacuum.

Spontaneous dark-matter mass generation along cosmological attractors in string theory

We propose a new scenario for generating a relic density of non-relativistic dark matter in the context of heterotic string theory. Contrary to standard thermal freeze-out scenarios, dark-matter particles are abundantly produced while still relativistic, and then decouple from the thermal bath due to the sudden increase of their mass above the universe temperature. This mass variation is sourced by the condensation of an order-parameter modulus, which is triggered when the temperature T (t) drops below the supersymmetry breaking scale M (t), which are both time-dependent. A cosmological attractor mechanism forces this phase transition to take place, in an explicit class of heterotic string models with spontaneously broken supersymmetry, and at finite temperature.

Sterile neutrinos in string derived models

The MiniBooNE collaboration recently reported further evidence for the existence of sterile neutrinos, implying substantial mixing with the left-handed active neutrinos and at a comparable mass scale. I argue that while sterile neutrinos may arise naturally in large volume string models, they prove more of a challenge in heterotic-string models that replicate the Grand Unified Theory structure of the Standard Model matter states. Sterile neutrinos in heterotic-string models may imply the existence of an additional Abelian gauge symmetry of order 10–100 TeV.

Spin-four mathcal{N}=7 W-supergravity: S-fold and double copy construction

In the present investigation we consider the possibility of having new massive, higher spin W-supergravity theories, which do not exist as four-dimensional perturbative models. These theories are based on a double copy construction of two supersymmetric field theories, where at least one factor is given by a mathcal{N}=3 field theory, which is a non-perturbative S-fold of mathcal{N}=4 super Yang-Mills theory. In this way, we can obtain as S-folds a new mathcal{N}=7 (corresponding to 28 supercharges) W-supergravity and its mathcal{N}=7 W-superstring counterpart, which both do not exist as four-dimensional perturbative models with an (effective) Langrangian description. The resulting field resp. string theory does not contain any massless states, but instead a massive higher spin-four supermultiplet of the mathcal{N}=7 supersymmetry algebra. Furthermore we also construct a four-dimensional heterotic S-fold with mathcal{N}=3 supersymmetry. It again does not exist as perturbative heterotic string model and can be considered as the heterotic counterpart of the mathcal{N}=3 superconformal field theories, which were previously constructed in the context of type I orientfold models.

GUT precursors and entwined SUSY: The phenomenology of stable nonsupersymmetric strings

Recent work has established a method of constructing non-supersymmetric string models that are stable, with near-vanishing one-loop dilaton tadpoles and cosmological constants. This opens up the tantalizing possibility of realizing stable string models whose low-energy limits directly resemble the Standard Model rather than one of its supersymmetric extensions. In this paper we consider the general structure of such strings and find that they share two important phenomenological properties. The first is a so-called "GUT-precursor" structure in which new GUT-like states appear with masses that can be many orders of magnitude lighter than the scale of gauge coupling unification. These states allow a parametrically large compactification volume, even in weakly coupled heterotic strings, and in certain regions of parameter space can give rise to dramatic collider signatures which serve as "smoking guns" for this overall string framework. The second is a residual "entwined-SUSY" (or e-SUSY) structure for the matter multiplets in which different multiplet components carry different horizontal $U(1)$ charges. As a concrete example and existence proof of these features, we present a heterotic string model that contains the fundamental building blocks of the Standard Model such as the Standard-Model gauge group, complete chiral generations, and Higgs fields --- all without supersymmetry. Even though massless gravitinos and gauginos are absent from the spectrum, we confirm that this model has an exponentially suppressed one-loop dilaton tadpole and displays both the GUT-precursor and e-SUSY structures. We also discuss some general phenomenological properties of e-SUSY, such as cancellations in radiative corrections to scalar masses, the possible existence of a corresponding approximate moduli space, and the prevention of rapid proton decay.

7a-K-10 TFD混成弦模型での宇宙項の相構造

7a-K-10 TFD混成弦模型での宇宙項の相構造

Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

The spinor–vector duality was discovered in free fermionic constructions of the heterotic string in four dimensions. It played a key role in the construction of heterotic–string models with an anomaly-free extra Z′ symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived Z′ model is via diphoton excess that may be within reach of the LHC. A fascinating possibility is that the spinor–vector duality symmetry is rooted in the structure of the heterotic–string compactifications to two dimensions. The two-dimensional heterotic–string theories are in turn related to the so-called moonshine symmetries that underlie the two-dimensional compactifications. In this paper, we embark on exploration of this connection by the free fermionic formulation to classify the symmetries of the two-dimensional heterotic–string theories. We use two complementary approaches in our classification. The first utilises a construction which is akin to the one used in the spinor–vector duality. Underlying this method is the triality property of SO(8) representations. In the second approach, we use the free fermionic tools to classify the twenty-four-dimensional Niemeier lattices.

Dilaton stabilization in three-generation heterotic string model

We study dilaton stabilization in heterotic string models. By utilizing the asymmetric orbifold construction, we construct an explicit three-generation model whose matter content in the visible sector is the supersymmetric standard model with additional vectorlike matter. This model does not contain any geometric moduli fields except the dilaton field. Model building at a symmetry enhancement point in moduli space enlarges the rank of the hidden gauge group. By analyzing multiple hidden gauge sectors, the dilaton field is stabilized by the racetrack mechanism. We also discuss a supersymmetry breaking scenario and F-term uplifting.

FlippedSU(5)string vacua classification: A variation of theSO(10)breaking basis vector

In this paper, an extension of the classification of flipped $SU(5)$ heterotic-string vacua from Faraggi, Rizos and Sonmez [Nucl. Phys. B886, 202 (2014)] with a variation of the $SO(10)$ breaking $\ensuremath{\alpha}$ basis vector is presented. A statistical sampling in the space of ${2}^{45}$ flipped $SU(5)$ vacua is explored, where ${10}^{11}$ distinct GGSO projection configurations are scanned in comparison to the ${10}^{12}$ GGSO distinct coefficients scanned in the space of ${2}^{44}$ vacua in Faraggi, Rizos and Sonmez. A JAVA code, akin to the one used for the classification in Faraggi, Rizos and Sonmez, was implemented to explore these. Results presented here indicate that no three-generation exophobic vacua exist, which was also found to be the case in Faraggi, Rizos and Sonmez as all odd generations were projected out. This paper will also study the details on the comparison between the two classifications achieved and reflect on the future directions in the quest for finding three-generation exophobic flipped $SU(5)$ heterotic-string models.

The 750 GeV di-photon LHC excess and extra $$Z^\prime $$ Z ′ 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 Z' models, where the di-photon excess may be connected with the Standard Model singlet scalar responsible for the Z' symmetry breaking, whereas the di-boson excess arises from production of the extra vector boson. Additional vector-like states in the string Z' model are instrumental to explain the relatively large width of the di-photon events and mandated by anomaly cancellation to be in the vicinity of the Z' breaking scale. Wilson line breaking of the non-Abelian gauge symmetries in the string models naturally gives rise to dark matter candidates. Future collider experiments will discriminate between the high-scale heterotic-string models, which preserve the perturbative unification paradigm indicated by the Standard Model data, versus the low scale string models. We also discuss the possibility for the production of the di-photon events with high scale $U(1)_{Z^\prime}$ breaking.

Discrete symmetries in the heterotic-string landscape

We describe a new type of discrete symmetry that relates heterotic-string models. It is based on the spectral flow operator which normally acts within a general N = (2, 2) model and we use this operator to construct a map between N = (2, 0) models. The landscape of N = (2, 0) models is of particular interest among all heterotic-string models for two important reasons: Firstly, N =1 spacetime SUSY requires (2, 0) superconformal invariance and secondly, models with the well motivated by the Standard Model SO(10) unification structure are of this type. This idea was inspired by a new discrete symmetry in the space of fermionic ℤ2 × ℤ2 heterotic-string models that exchanges the spinors and vectors of the SO(10) GUT group, dubbed spinor-vector duality. We will describe how to generalize this to arbitrary internal rational Conformal Field Theories.

Light U(1)s in heterotic string models

We present a novel string-derived U(1) combination that satisfies necessary properties to survive to low scales. We discuss previous attempts at acquiring such an abelian gauge symmetry from two different string embeddings and the pitfalls associated with them. Finally, we give an example of how a satisfactory model may be constructed within our framework.

Thermal duality and gravitational collapse

Thermal duality is a relationship between the behaviour of heterotic string models of the E(8)×E(8) or SO(32) types at inversely related temperatures, a variant of T duality in the Euclidean regime. This duality would have consequences for the nature of the Hagedorn transition in these string models. We propose that the vacuum admits a family of deformations in situations where there are closed surfaces of constant area but high radial acceleration (a string regularized version of a Penrose trapped surface), such as would be formed in situations of extreme gravitational collapse. This would allow a radical resolution of the firewall paradox by allowing quantum effects to significantly modify the spacetime geometry around a collapsed object. A string bremsstrahlung process would convert the kinetic energy of infalling matter in extreme gravitational collapse to form a region of the deformed vacuum, which would be equivalent to forming a high temperature string phase. A heuristic criterion for the conversion process is presented, relating Newtonian gravity to the string tension, suggesting an upper limit to the strength of the gravitational interaction. This conversion process might have observable consequences for charged particles falling into a rotating collapsed object by producing high energy particles via a variant of the Penrose process.

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.

Heterotic QCD axion

We show that a KSVZ axion with a decay constant in the phenomenologically allowed range can be obtained in certain $E_8\times E_8$ heterotic string models. These models have an enhanced symmetry locus in the moduli space, and a non-universal, Kahler moduli dependent Fayet-Iliopoulos term which vanishes at this locus. Close to this locus the Fayet-Iliopoulos term is small and can lead to an axion decay constant significantly lower than the string scale. In this way, the no-go arguments of Svrcek and Witten, which are based on a universal, dilaton-dependent Fayet-Iliopoulos term, can be avoided. The relevant axion originates from phases of bundle moduli which correspond to deformations away from the enhanced symmetry locus. We construct an explicit example, based on a heterotic line bundle standard model, with all the required ingredients.

Spectral flow as a map between [formula omitted]-models

The space of (2,0) models is of particular interest among all heterotic-string models because it includes the models with the minimal SO(10) unification structure, which is well motivated by the Standard Model of particle physics data. The fermionic Z2×Z2 heterotic-string models revealed the existence of a new symmetry in the space of string configurations under the exchange of spinors and vectors of the SO(10) GUT group, dubbed spinor–vector duality. In this paper we generalize this idea to arbitrary internal rational conformal field theories (RCFTs). We explain how the spectral flow operator normally acting within a general (2,2) theory can be used as a map between (2,0) models. We describe the details, give an example and propose more simple currents that can be used in a similar way.