arXiv subjects

Alon E. Faraggi

Publications and source records attributed to Alon E. Faraggi.

At least 19 recordsLinked to original sources

arXiv2026

Classification of order-two T-duality orbifolds at the SO(12) free fermionic point

Asymmetric orbifolds provide concrete examples of non-geometric constructions dubbed T-folds. All Z2 point groups of six dimensional asymmetric order-two orbifolds are identified. The order-two T-fold configurations on the SO(12) lattice are classified at the fermionic point of type II string theories for all Z2 point groups. The spectra of the models on these configurations are presented parametrically, in terms of certain generalised GSO phases. The minimal effective Hodge numbers were found to be (h_{11},h_{12})=(1,1) for six T-fold configurations. Asymmetric generalisations of the mirror symmetry map are conjectured. The orientifoldable configurations using the basic worldsheet parity were identified within the classification. Twisted sectors corresponding to pure asymmetric twists may contain Rarita-Schwinger multiplets with spin-3/2 states. Throughout the paper, generalised GSO projections are chosen to preserve the maximal amount of supersymmetry possible. Relaxing this, the order-two point groups were identified for which non--supersymmetric T-folds can be constructed. Since some of them may enhance to N=1 or, even, N=2 supergravities, we argue that appearance of spin-3/2 states necessarily implies that the spectrum has reorder itself in a supersymmetric fashion and hence that the vacuum energy vanishes.

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arXiv2026

Classification of Pati--Salam Asymmetric $\mathbb{Z}_2 \times \mathbb{Z}_2$ Heterotic String Orbifolds

We develop a systematic classification of asymmetric $\mathbb{Z}_2$ orbifold actions in Pati-Salam heterotic string vacua constructed in the free fermionic formulation. Starting from symmetric $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$ orbifold vacua with an $SO(10)$ GUT, we allow the Pati--Salam breaking vector to act asymmetrically on the internal degrees of freedom. The asymmetric orbifold action freezes geometrical moduli whilst inducing doublet--triplet splitting in the untwisted sector. Notably, this doublet-triplet splitting operates for any asymmetric action, including pure asymmetric shifts that preserve all geometric moduli, and is therefore independent of moduli stabilisation. Classifying the breaking vector according to its twist action, we find six inequivalent classes of geometric moduli spaces characterised by 12, 8, 4 or 0 real untwisted moduli. Through combining these asymmetric twists with all compatible asymmetric shifts, 24 inequivalent cases are identified and characterised by their residual moduli content and internal Narain lattice. For each case we construct representative basis sets admitting three chiral generations, providing the starting point for further classification within each class. We perform explicit GGSO (generalized Gliozzi-Scherk-Olive) phase enumerations in representative model classes with 12, 8, 4 and 0 moduli, classify the resulting $\mathcal{N}=1$ and $\mathcal{N}=0$ vacua according to phenomenological criteria and identify exophobic, phenomenologically viable models. We compute the partition function and corresponding one-loop vacuum energy at the free fermionic point in moduli space for each phenomenologically viable model across the four classes. As the number of geometrical moduli decreases, the number of distinct partition functions for these vacua collapses to a small number, reflecting a pronounced degeneracy under GGSO phase variations.

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arXiv2026

Fundamental or Composite? The Higgs Enigma

The discovery of the Higgs boson by the ATLAS and CMS experiments concluded a glorious century of experimental particle physics discoveries, from Rutherford's discovery of the nucleus in 1911, through the discoveries of quarks and leptons from the 1950s to the 1970s, to the discoveries of the weak vector bosons in the 1980s. It cemented the Standard Model of particle physics as providing the viable parameterisation of all sub-atomic observables up to the TeV scale and possibly up to the GUT and Planck scales. The experimental determination of the Higgs properties and parameters will shed light on these fundamental theories. A particularly pertaining question from the point of view of String Phenomenology is whether the Higgs boson is a fundamental or composite particle. The fermionic Z2xZ2 orbifolds provide bench mark models to explore how the parameters of the Standard Model can arise from a theory of quantum gravity, as well as for physics Beyond the Standard Model. Observation that the Higgs is composite will nullify much of the work that have gone into heterotic string model building over the past 40 years and will indicate the relevance of other classes of string vacua or possibly other approaches to quantum gravity. An ideal facility in the near future to investigate this question is a hadron collider at 50-60 TeV that utilises contemporary magnet technology and can be built in 10-15 years from decision.

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arXiv2025

A Perturbatively Stable Non-Supersymmetric String Model with AdS Vacuum

We present a construction of a perturbatively stable non-supersymmetric type II closed string model in four dimensions. It is based on a freely acting Scherk-Schwarz Z2-deformation of a supersymmetric construction which is recovered in appropriate decompactification limits. The model exhibits also the so-called misaligned supersymmetry with alternating signs for the number difference between bosons and fermions at successive mass levels. The tree-level spectrum is tachyon free for any value of the radii and moduli. At one loop level, the scalar potential has a non-supersymmetric minimum at the self-dual (free fermionic) point with negative energy, around which all tree-level massless scalars acquire positive masses. The model is thus non-supersymmetric and perturbatively stable.

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arXiv2025

Mirror Symmetry and Spinor-Vector Duality: A Top-Down Approach to the Swampland Program

Mirror symmetry is one of the celebrated developments in pure mathematics that arose from an initial observation in worldsheet string constructions. The profound implications of mirror symmetry in the Effective Field Theory (EFT) limit of string compactifications was subsequently understood. In particular, it proved to be an exceptionally useful tool in the field of enumerative geometry. Spinor-Vector Duality (SVD) is an extension of mirror symmetry that can be readily understood in terms of the moduli parameters of toroidal heterotic-string compactifications, which include the metric, the anti-symmetric ternsor field and the Wilson-line moduli. While mirror symmetry corresponds to maps of the internal moduli parameters, {ı.e.} the metric and the anti-symmetric tensor field, SVD corresponds to maps of the Wilson-line moduli. Similar to mirror symmetry the imprint of SVD in the EFT limit can serve as a tool to study the properties of complex manifolds with vector-bundles. Spinor-Vector Duality motivates a top--down approach to the "Swampland" program, by studying the imprint of the symmetries of the worldsheet ultra-violet complete string constructions in the EFT limit. It is conjectured that SVD provides a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding in string theory versus those that do not.

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arXiv2025

Experimental Particle Physics Priorities 2025: A String Phenomenology Perspective

With the SNOWMASS 2021 process in the US and the on--going European Strategy Report 2025, the field of elementary particle physics is undergoing detailed community evaluation, and the experimental particle physics program, which requires substantial public investment, is under scrutiny. We offer an assessment of the current experimental particle physics priorities from a string phenomenology point of view. String theory provides a perturbatively consistent framework for quantum gravity. String phenomenology aims to connect between string theory and observational data. String theory is a consistent theory of quantum gravity that contains the other fundamental constituents of matter and interactions. As all forms of energy couple to gravity, string theory provides a framework that reproduces the structures of the Standard Model of particle physics and gives rise to detailed physics scenarios beyond the Standard Model, {\it e.g.} dark matter candidates, axions, additional gauge symmetries, etc. Given this breadth, we propose that from a string phenomenology perspective, the experimental particle physics priority is the nature of the Higgs boson and the electroweak symmetry breaking mechanism. An ideal facility in the near future to study this sector is a hadron collider at 50--60 TeV that utilises contemporary magnet technology and can be built in 10--15 years from decision.

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arXiv2025

The Quest for Understanding: The Case of the Upgraded Superconducting Super Collider

Fundamental particle physics is at a cross road. On the one hand the Standard Model successfully accounts for all experimental observations to date. On the other hand the ElectroWeak symmetry breaking mechanism is poorly understood and suggests the existence of new physics within reach of future colliders. Building on LHC experience, a hadron collider using the well established LHC magnet technology in a 90--100km circular ring, can reach the required 50--60TeV energy range and uncover the next layers of reality by the early 2040s.

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arXiv2025

Vacuum Energy in Non-Supersymmetric Quasi-Realistic Heterotic-String Vacua with Fixed Moduli

Recently, Baykara, Tarazi and Vafa discussed the existence of quasicrystalline string vacua that contain a single neutral moduli, the dilaton, and studied compactifications of the non-supersymmetric $SO(16)\times SO(16)$ heterotic-string on these spaces. We discuss a specific class of quasi-realistic string vacua with similar properties that has been known since the late eighties and analyse the vacuum energy in several non-supersymmetric examples that correspond to compactifications of tachyon free ten dimensional vacua as well as compactifications of tachyonic ten dimensional vacua. Our analysis uses the Free Fermionic Formalism of the heterotic-string in four dimensions and employs asymmetric boundary conditions that project all the geometrical moduli by Generalised GSO projections. This methodology produces models with both positive and negative spacetime potential at one-loop.

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arXiv2024

Spinor-Vector Duality and Mirror Symmetry

Mirror symmetry was first observed in worldsheet string constructions and shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi-Yau manifolds. It opened up a new field in pure mathematics and was utilised in the area of enumerative geometry. Spinor-Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the heterotic string, which include the metric the antisymmetric tensor field and the Wilson line moduli. In terms of toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas spinor-vector duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of spinor-vector duality in the effective field theory compactifications of the string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited spinor-vector duality and resolving the orbifold singularities, hence generating a smooth effective field theory limit with an imprint of the spinor-vector duality. Just like mirror symmetry, the spinor-vector duality can be used to study the properties of complex manifolds with vector bundles. Spinor--vector duality offers a top-down approach to the ``Swampland''-program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not.

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arXiv2024

Vacuum Energy of Non-Supersymmetric $\mathbf{\tilde{S}}$ Heterotic String Models

We use the free fermionic formulation of the heterotic-string in four dimensions to study the vacuum structure and energy of non-supersymmetric tachyon free models that correspond to compactifications of tachyonic vacua of the ten dimensional heterotic-string. We explore the class of heterotic $SO(10)$ non-supersymmetric models constructed from the $\tilde{S}$-model in the Free Fermionic Formalism, and investigate the dependence of the potential on the geometric moduli. This paper will explore a sample of $ 10^{9}$ string vacua to find the frequency of viable models, classifying these vacua by the following fertility criteria: tachyon presence; number of spinorial $\boldsymbol{16/\overline{16}}$ representations; vectorial $\boldsymbol{10}$ states; Top Quark Mass Coupling compatibility. Of these we find those that mimic supersymmetric models with equal number of bosons and fermions at the massless level - $a_{00} = 0$. Tachyon free models occur with a frequency of $5.309\times10^{-3}$. Furthermore, models that fulfil the rest of the phenomenological fertility conditions and the additional condition on $a_{00}$ occur with probability $4.0 \times 10^{-9}$ We analyse the partition functions and study the moduli dependence of such models, finding that almost all fertile models have finite, positive potential at the Free Fermionic Point, with $2$ out of $84$ of the fertile cores having negative, finite potential. We demonstratate that the Free Fermionic Point is not necessarily a minimum in the potential. This work provides further evidence that supersymmetry may not be a necessary ingredient of phenomenological models, recreating many of the desirable features of such models without employing supersymmetry.

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arXiv2024

Fayet-Iliopoulos D-Term in Non-Supersymmetric Heterotic String Orbifolds

The Fayet-Iliopoulos $D$-term is a common feature in $\mathcal{N}=1$ string vacua that contain an anomalous $U(1)$ gauge symmetry, and arises from a one--loop diagram in string perturbation theory. The same diagram is generated in string vacua in which supersymmetry is broken directly at the string scale, either via spontaneous Scherk-Schwarz breaking, in which case the gravitino mass is determined by the radius of the circle used in the Scherk-Schwarz mechanism, or via explicit supersymmetry breaking by the GSO projections. We analyse the resulting would-be Fayet-Illiopoulos $D$-term in the non-supersymmetric string vacua and its contribution to the vacuum energy. A numerical estimate in an explicit tachyon-free string-derived model suggests that the would-be $D$-term contribution may uplift the vacuum energy to a positive value.

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arXiv2024

Free fermionic webs of heterotic T-folds

Moduli stabilisation is key to obtaining phenomenologically viable string models. Non-geometric compactifications, like T-duality orbifolds (T-folds), are capable of freezing many moduli. However, in this Letter we emphasise that T-folds, admitting free fermionic descriptions, can be associated with a large number of different T-folds with varying number of moduli, since the fermion pairings for bosonisation are far from unique. Consequently, in one description a fermionic construction might appear to be asymmetric, and hence non-geometric, while in another it admits a symmetric orbifold description. We introduce the notion of intrinsically asymmetric T-folds for fermionic constructions that do not admit any symmetric orbifold description after bosonisation. Finally, we argue that fermion symmetries induce mappings in the bosonised description that extend the T-duality group.

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arXiv2023

$M_W$ in String Derived $Z'$ Models

We introduce a phenomenological model for a string-derived $Z'$ scenario, and study its predictions for the mass of the W boson. In the process, we compare it to collider constraints for both pair-produced particles, Higgs boson properties, and $Z'$ searches. We also describe the implementation of new tools in the scanning code BSMArt.

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arXiv2023

String Derived Z$^\prime$ Model at an Upgraded Superconducting Super Collider

The future of collider physics is under investigation. With the High Luminosity LHC program lasting until the late 2030s, the next machine in the energy frontier is envisioned to appear in 30--40 years, which may be too far into the future to sustain the field. In this paper we explore the physics potential of an Upgraded Superconducting Super Collider (USSC). The Original Superconducting Super Collider (OSSC) was planned to operate at 20TeV beam energy, and with improved magnet technology and/or longer tunnel, one may envision that it can be extended to 25--30TeV beam energy. Given that the decision on the OSSC construction took place in Autumn 1988 and it was planned to start operation in the 1996-1999 period, an USSC can be constructed 10--15 years from decision and fill the gap between the end of HL--LHC and the future envisioned machines. While the main mission of the USSC will be to test the Standard Model and its electroweak and strongly interacting sectors, as a specific example we illustrate the invariant mass distribution at NNLO in QCD for a 5 TeV $Z^\prime$ in the string derived $Z^\prime$ model.

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arXiv2023

D-term Uplifts in Non-Supersymmetric Heterotic String Models

Recently, we proposed that the one-loop tadpole diagram in perturbative non-supersymmetric heterotic string vacua that contain an anomalous $U(1)$ symmetry, leads to an analog of the Fayet-Iliopoulos $D$-term in $\mathcal{N}=1$ supersymmetric models, and may uplift the vacuum energy from negative to positive value. In this paper, we extend this analysis to new types of vacua, including those with Stringy Scherk-Schwarz (SSS) spontaneous supersymmetry breaking versus those with explicit breaking. We develop a criteria that facilitates the extraction of vacua with Scherk-Schwarz breaking. We develop systematic tools to analyse the T-duality property of some of the vacua and demonstrate them in several examples. The extraction of the anomalous $U(1)$ $D$-terms is obtained in two ways. The first utilises the calculation of the $U(1)$-charges from the partition function, whereas the second utilises the free fermionic classification methodology to classify large spaces of vacua and analyse the properties of the massless spectrum. The systematic classification method also ensures that the models are free from physical tachyons. We provide a systematic tool to relate the free fermionic basis vectors and one-loop Generalised GSO phases that define the string models, to the one-loop partition function in the orbifold representation. We argue that a $D$-term uplift, while rare, is possible for both the SSS class of models, as well as in those with explicit breaking. We discuss the steps needed to further develop the arguments presented here.

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arXiv2023

Precision studies for string derived $Z'$ dynamics at the LHC

We consider $Z'$s in heterotic string derived models and study $Z'$ resonant production at the TeV scale at the Large Hadron Collider (LHC). We use various kinematic differential distributions for the Drell-Yan process at NNLO in QCD to explore the parameter space of such models and investigate $Z'$ couplings. In particular, we study the impact of $Z$-$Z'$ kinetic-mixing interactions on forward-backward asymmetry ($A_{FB}$) and other distributions at the LHC.

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arXiv2022

Spinor-Vector Duality and the Swampland

The Swampland Program aims to address the question, "when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?", and can be regarded as a bottom-up approach to investigations of quantum gravity. An alternative top-down approach aim to explore the imprints and the constraints imposed by the string theory dualities and symmetries on the effective field theory representations of quantum gravity. The most celebrated example of this approach is mirror symmetry. Mirror symmetry was first observed in worldsheet contructions of string compactifications. It was completely unexpected from the effective field theory point of view, and its implications in that context were astounding. In terms of the moduli parameters of toroidally compactified Narain spaces, mirror symmetry can be regarded as arising from mappings of the moduli of the internal compactified space. Spinor-vector duality, which was discovered in worldsheet constructions of string vacua, is an extension of mirror symmetry that arises from mappings of the Wilson line moduli, and provide a probe to constrain and explore the moduli spaces of $(2,0)$ string compactifications. Mirror symmetry and spinor-vector duality are mere two examples of a much wider symmetry structure, whose implications are yet to be unravelled. A mapping between supersymmetric and non-supersymmetric vacua is briefly discussed. $T$-duality is another important property of string theory, and can be thought of as phase-space duality in compact space. I propose that manifest phase-space duality, and the related equivalence postulate of quantum mechanics, provide the background independent overarching principles underlying quantum gravity.

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arXiv2022

Towards Classification of $\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped $SU(5)$ Asymmetric $\mathbb{Z}_2 \times \mathbb{Z}_2$ Heterotic String Orbifolds

The free fermionic classification method provides a powerful tool to investigate string vacua, which led to the discovery of spinor--vector duality and exophobic string models. We extend the classification methodology to both $\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped $SU(5)$ $\mathbb{Z}_2 \times \mathbb{Z}_2$ heterotic string orbifolds with asymmetric shifts. The impact of the asymmetric assignments on the phenomenological characteristics of these models is investigated. Of particular interest is the analysis of untwisted moduli fixing for various choices of asymmetric boundary conditions. Two classes of vacua with different characteristics are systematically investigated with help from SAT/SMT algorithms, which are shown to increase search efficiency by up to two orders of magnitude, as well as providing useful tools to find contradictions between various phenomenological criteria. The general form of the partition function for the space of models is explained and given for two specific example models for different choices of asymmetric boundary conditions. Additionally, the distribution of one-loop cosmological constant contributions for samples in the two different classes of models are depicted and discussed.

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