arXiv subjects

John Rizos

Publications and source records attributed to John Rizos.

At least 19 recordsLinked to original sources

arXiv2024

Free Fermionic Constructions of Heterotic Strings

This chapter is an introduction to the Free Fermionic Formulation of String Theory, with emphasis on heterotic model building. After a brief review of bosonization in two dimensional conformal field theories, we discuss how internal bosonic string coordinates can be consistently replaced by free fermionic degrees of freedom. In this framework, worldsheet supersymmetry may be realized entirely among free fermions. Embedding this construction into string theory leads to a number of constraints arising from modular invariance at one and higher genera. The solution of these constraints takes the form of a small number of model building rules from which the string spectrum and interactions may be analyzed. We review some of the most well-studied models in the literature and their classification, with emphasis on the symmetric basis. The explicit map of free fermionic models to the orbifold construction is presented in some detail.

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arXiv2023

From Free-Fermionic Constructions to Orbifolds and Back

We systematically develop the explicit map between string vacua constructed in the Free Fermionic Formulation and their $\mathbb{Z}_2^N$ toroidal orbifold counterparts. We illustrate the map in various example classes of models, including cases relevant for string phenomenology, as well as in theories where space-time supersymmetry is broken by the stringy Scherk-Schwarz mechanism.

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arXiv2023

String Model Building on Quantum Annealers

We explore for the first time the direct construction of string models on quantum annealers, and investigate their efficiency and effectiveness in the model discovery process. Through a thorough comparison with traditional methods such as simulated annealing, random scans, and genetic algorithms, we highlight the potential advantages offered by quantum annealers, which in this study promised to be roughly fifty times faster than random scans and genetic algorithm and approximately four times faster than simulated annealing.

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arXiv2022

Particle physics and cosmology of the string derived no-scale flipped $SU(5)$

In a recent paper, we identified a cosmological sector of a flipped $SU(5)$ model derived in the free fermionic formulation of the heterotic superstring, containing the inflaton and the goldstino superfields with a superpotential leading to Starobinsky type inflation, while $SU(5){\times}U(1)$ is still unbroken. Here, we study the properties and phenomenology of the vacuum after the end of inflation, where the gauge group is broken to the Standard Model. We identify a set of vacuum expectation values, triggered by the breaking of an anomalous $U(1)_A$ gauge symmetry at roughly an order of magnitude below the string scale, that solve the F and D-flatness supersymmetric conditions up to 6th order in the superpotential which is explicitly computed, leading to a successful particle phenomenology. In particular, all extra colour triplets become superheavy guaranteeing observable proton stability, while the Higgs doublet mass matrix has a massless pair eigenstate with realistic hierarchical Yukawa couplings to quarks and leptons. The supersymmetry breaking scale is constrained to be high, consistent with the non observation of supersymmetric signals at the LHC.

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arXiv2022

Three-Generation Super No-Scale Models in Heterotic Superstrings

We derive the conditions for the one-loop contribution to the cosmological constant to be exponentially suppressed in a class of heterotic string compactifications with three generations of chiral matter, where supersymmetry is spontaneously broken à la Scherk-Schwarz. Using techniques of partial unfolding based on the Hecke congruence subgroup $Γ_0(2)$ of the modular group to extract the leading asymptotics, we show that the super no-scale condition $n_B=n_F$ between the degeneracies of massless bosons $n_B$ and fermions $n_F$ in the full string spectrum is necessary but not sufficient, and needs to be supplemented by additional conditions which we identify. We use these results to construct three-generation Pati-Salam models with interesting phenomenological characteristics.

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arXiv2021

Super No-Scale Models with Pati-Salam Gauge Group

We construct and classify heterotic models where $\mathcal N=1$ supersymmetry is spontaneously broken à la Scherk-Schwarz. The theories contain chiral matter transforming under an observable Pati-Salam gauge symmetry and are classified according to a minimal set of phenomenological requirements, including the shape of their one-loop effective potential. The latter is essentially controlled by two parameters that are easily computable in terms of the defining string data. By imposing Bose-Fermi degeneracy at the massless level, known as the super no-scale condition, it is possible to suppress the value of the effective potential to exponentially small values, provided the compactification scale is sufficiently lower than the string scale. Furthermore, we compare the space of $\sim 10^{10}$ Pati-Salam models with their parent theories based on SO(10) gauge symmetry and confirm the universality structure of their effective one-loop potentials.

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arXiv2021

Cosmology of the string derived flipped $SU(5)$

We study the cosmology of a string derived supersymmetric flipped $SU(5)$ model in the context of free-fermionic heterotic constructions that allow full calculability of the effective supergravity in perturbation theory around the fermionic vacuum where all string moduli have fixed values. The model has 3 generations of chiral families and a Higgs sector leading to particle phenomenology consistent with low energy data, that has been extensively studied in the past. Here, we show that it can also accommodate a novel successful cosmology, based on the no-scale effective supergravity derived from string theory as well as an appropriate induced superpotential suppressed by five powers of the string scale. It utilises two gauge singlet chiral superfields present in the low energy spectrum: the inflaton $y$, identified as the superpartner of a state mixed with R-handed neutrinos, and the goldstino $z$ with a superpotential of the form $W_I=M_I z(y-λy^2)$ (in supergravity units) where $λ$ is a dimensionless ${\cal O}\left(1\right)$ parameter and $M_I$ the mass scale of inflation generated at 5th order by the breaking of an anomalous $U(1)_A$ gauge symmetry, characteristic of heterotic string chiral vacua. The resulting scalar potential leads to Starobinsky type inflation. Our results can be easily generalised to a large class of models with similar properties.

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arXiv2020

Doublet-Triplet Splitting in Fertile Left-Right Symmetric Heterotic String Vacua

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 $4\times 10^{-11}$. 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 $1.4\times 10^{-2}$, hence increasing the probability of generating phenomenologically viable models by nine orders of magnitude, and producing some $1.4\times 10^5$ 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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arXiv2019

Towards machine learning in the classification of Z2xZ2 orbifold compactifications

Systematic classification of Z2xZ2 orbifold compactifications of the heterotic-string was pursued by using its free fermion formulation. The method entails random generation of string vacua and analysis of their entire spectra, and led to discovery of spinor-vector duality and three generation exophobic string vacua. The classification was performed for string vacua with unbroken SO(10) GUT symmetry, and progressively extended to models in which the SO(10) symmetry is broken to the SO(6)xSO(4), SU(5)xU(1), SU(3)xSU(2)xU(1)^2 and SU(3)xU(1)xSU(2)^2 subgroups. Obtaining sizeable number of phenomenologically viable vacua in the last two cases requires identification of fertility conditions. Adaptation of machine learning tools to identify the fertility conditions will be useful when the frequency of viable models becomes exceedingly small in the total space of vacua.

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arXiv2018

Classification of Left-Right Symmetric Heterotic String Vacua

The classification method of the free fermionic heterotic string vacua is extended to models where the $SO(10)$ GUT symmetry is broken directly at the string scale to the Left-Right Symmetric subgroup. Our method involves using a fixed set of basis vectors which are defined by the boundary conditions assigned to the free fermions before enumerating the string vacua by varying the Generalised GSO (GGSO) projection coefficients. It allows the derivation of algebraic expressions for the GGSO projections for each sector that generates massless states in the models. This enables a computerised analysis of the entire massless spectrum of a given choice of GGSO projection coefficients. The total number of vacua in the class of models chosen is $2^{66}\approx 7.38 \times 10^{19}$. A statistical sampling is performed and a sample size of $10^{11}$ vacua with the Left-Right Symmetric gauge group is extracted. We present the results of the classification, noting that contrary to the previous classification of Pati-Salam models, no three generation exophobic models were found. The results obtained demonstrate the existence of three generation models with the necessary Higgs representations needed for viable spontaneous symmetry breaking, and with a leading top quark Yukawa coupling.

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arXiv2017

Classification of Standard-like Heterotic-String Vacua

We extend the free fermionic classification methodology to the class of standard-like heterotic-string vacua, in which the $SO(10)$ GUT symmetry is broken at the string level to $SU(3)\times SU(2)\times U(1)^2$. The space of GGSO free phase configurations in this case is vastly enlarged compared to the corresponding $SO(6)\times SO(4)$ and $SU(5)\times U(1)$ vacua. Extracting substantial numbers of phenomenologically viable models therefore requires a modification of the classification methods. This is achieved by identifying conditions on the GGSO projection coefficients, which are satisfied at the $SO(10)$ level by random phase configurations, and that lead to three generation models with the $SO(10)$ symmetry broken to the $SU(3)\times SU(2)\times U(1)^2$ subgroup. Around each of these fertile $SO(10)$ configurations, we perform a complete classification of standard-like models, by adding the $SO(10)$ symmetry breaking basis vectors, and scanning all the associated GGSO phases. Following this methodology we are able to generate some $10^7$ three generation Standard-like Models. We present the results of the classification and one exemplary model with distinct phenomenological properties, compared to previous SLM constructions.

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arXiv2017

A Solution to the Decompactification Problem in Chiral Heterotic Strings

We present a solution to the decompactification problem of gauge thresholds in chiral heterotic string theories with two large extra dimensions, where supersymmetry is spontaneously broken by the Scherk-Schwarz mechanism. Whenever the Kaluza-Klein scale is much lower than the string scale, the infinite towers of heavy states contribute non-trivially to the renormalisation of gauge couplings, which typically grow linearly with the large volume of the internal space and invalidate perturbation theory. We trace the origin of the decompactification problem to properties of the six dimensional theory obtained in the infinite volume limit and show that thresholds may instead exhibit logarithmic volume dependence and we provide the conditions for this to occur. We illustrate this mechanism with explicit string constructions where the decompactification problem does not occur.

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arXiv2016

Chiral Heterotic Strings with Positive Cosmological Constant

We present explicit examples of semi-realistic heterotic models with spontaneously broken supersymmetry, which dynamically lead to breaking scales much smaller than $M_{\rm Planck}$ and exponentially small positive values for the cosmological constant. Contrary to field theoretic intuition, we find that the global structure of the effective potential is significantly affected by contributions of massive and non-level matched string states and we investigate the conditions that dynamically ensure a number of desired properties.

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arXiv2016

The 750 GeV diphoton LHC excess and Extra 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.

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arXiv2015

Spinor-vector duality and light Z' in heterotic string vacua

We discuss the construction of heterotic--string models that allow for the existence of an extra $Z^\prime$ at low scales. One of the main difficulties encountered is that the desired symmetries tend to be anomalous in the prevailing three generation constructions. The reason is that these models utilise the symmetry breaking pattern $E_6\rightarrow SO(10)\times U(1)_ζ$ by GGSO projections. Consequently, $U(1)_ζ$ becomes anomalous. The spinor--vector duality that was observed in the fermionic $Z_2\times Z_2$ orbifold compactifications is used to construct a phenomenological three generation Pati--Salam heterotic--string model in which $U(1)_ζ$ is anomaly free and therefore can be a component of a low scale $Z^\prime$. The model implies existence of matter states at the $Z^\prime$ breaking scale, which are required for anomaly cancelation. Moreover, the string model gives rise to exotic states, which are $SO(10)$ singlets but carry exotic $U(1)_ζ$ charges. These states arise due to the breaking of $E_6$ by discrete Wilson lines and provide natural dark matter candidates. Initial indications suggest that the existence of additional gauge symmetries at the TeV scale may be confirmed in run II of the LHC experiment.

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arXiv2015

A Light Z' 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 $SU(4)_C\times SU(2)_L\times SU(2)_R\times U(1)_ζ$, 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 $B-L$, $T_{3_L}$ and $T_{3_R}$. 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 states arise in the string model due to the breaking of the E6 symmetry by discrete Wilson lines. They represent a distinct signature of the string vacua and cannot arise in E6 Grand Unified Theories. They may provide viable dark matter candidates.

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arXiv2014

Genetic Algorithms and the Search for Viable String Vacua

Genetic Algorithms are introduced as a search method for finding string vacua with viable phenomenological properties. It is shown, by testing them against a class of Free Fermionic models, that they are orders of magnitude more efficient than a randomised search. As an example, three generation, exophobic, Pati-Salam models with a top Yukawa occur once in every 10^{10} models, and yet a Genetic Algorithm can find them after constructing only 10^5 examples. Such non-deterministic search methods may be the only means to search for Standard Model string vacua with detailed phenomenological requirements.

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arXiv2014

Classification of Flipped SU(5) Heterotic-String Vacua

We extend the classification of the free fermionic heterotic-string vacua to models in which the SO(10) GUT symmetry at the string scale is broken to the flipped SU(5) subgroup. In our classification method, the set of basis vectors defined by the boundary conditions which are assigned to the free fermions is fixed and the enumeration of the string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the analysis of the entire string spectrum to be programmed in to a computer code therefore, we performed a statistical sampling in the space of 2^{44} (approximately 10^{13}) flipped $SU(5)$ vacua and scanned up to 10^{12} GGSO configurations. For that purpose, two independent codes were developed based on JAVA and FORTRAN95. All the results presented here are confirmed by the two independent routines. Contrary to the corresponding Pati-Salam classification, we do not find exophobic flipped SU(5) vacua with an odd number of generations. We study the structure of exotic states appearing in the three generation models that additionally contain a viable Higgs spectrum. Moreover, we demonstrate the existence of models in which all the exotic states are confined by a hidden sector non-Abelian gauge symmetry as well as models that may admit the racetrack mechanism.

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