In this paper we show how some flavor symmetries may be derived from the heterotic string, when compactified on a 6D orbifold. In the body of the paper we focus on the $D_4$ family symmetry, recently obtained in $Z_3 \times Z_2$ orbifold constructions. We show how this flavor symmetry constrains fermion masses, as well as the soft SUSY breaking mass terms. Flavor symmetry breaking can generate the hierarchy of fermion masses and at the same time the flavor symmetry suppresses large flavor changing neutral current processes.
Heterotic orbifolds can explain the origin of flavor symmetries and the flavor representations of matter fields in particle physics as a result of the geometric properties of the associated string states in the compact space. After a review of the method to obtain flavor symmetries in these models, we determine the most frequent non-Abelian flavor symmetries appearing in promising Abelian heterotic orbifolds. Interestingly, these symmetries correspond only to D_4, Delta(54) and products of these symmetries and Abelian factors. A large set of promising models exhibits purely Abelian flavor symm…
A glossary overview of the phenomenological studies of quasi-realistic free fermionic heterotic string models is presented. I elaborate on the correspondence of these models with Z2XZ2 orbifolds.
Modular transformations of string theory (including the well-known stringy dualities) play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They are at the origin of CP transformations and provide a unification of CP with traditional flavor symmetries. Here, we present a novel, fully systematic method to reliably compute the unified flavor symmetry of the low-energy effective theory, including enhancements from the modular transformations of string theory. The unified flavor group is non-universal in moduli space and exhibits the phenomenon of "Local Flavor…
We study the minimal flavor violation in the context of string effective field theory. Stringy selection rules indicate that $n$-point couplings among fermionic zero-modes and lightest scalar modes in the string effective action are given by a product of Yukawa couplings which are regarded as spurion fields of stringy and geometrical symmetries. Hence, Yukawa couplings determine the dynamics of flavor and CP violations. This observation strongly supports the hypothesis of minimal flavor violation in the Standard Model effective field theory.
Modular transformations of string theory are shown to play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They include CP transformations and provide a unification of CP with traditional flavor symmetries within the framework of the "eclectic flavor" scheme. The unified flavor group is non-universal in moduli space and exhibits the phenomenon of "Local Flavor Unification", where different sectors of the theory (like quarks and leptons) can be subject to different flavor structures.
We study the flavor structure in $SO(32)$ heterotic string theory on six-dimensional torus with magnetic fluxes. In particular, we focus on models with the flavor symmetries $SU(3)_f$ and $Δ(27)$. In both models, we can realize the realistic quark masses and mixing angles.
We construct a string-inspired model, motivated by the flavored Peccei-Quinn (PQ) axions, as a useful bridge between flavor physics and string theory. The key feature is two anomalous gauged $U(1)$ symmetries, responsible for both the fermion mass hierarchy problem of the standard model and the strong CP problem, that combine string theory with flavor physics and severely constrain the form of the F- and D-term contributions to the potential. In the context of supersymmetric moduli stabilization we stabilize the size moduli with positive masses while leaving two axions massless and one axion m…
String theory leads to a flavor scheme where modular symmetries play a crucial role. Together with the traditional flavor symmetries they combine to an eclectic flavor group, which we determine via outer automorphisms of the Narain space group. Unbroken flavor symmetries are subgroups of this eclectic group and their size depends on the location in moduli space. This mechanism of local flavor unification allows a different flavor structure for different sectors of the theory (such as quarks and leptons) and also explains the spontaneous breakdown of flavor- and CP-symmetries (via a motion in m…
We investigate supersymmetric models in which an anomalous $U(1)_{X}$ symmetry explains the Yukawa hierarchy, and the related $D_{X}$-term plays a role in supersymmetry breaking. We use a bottom-up approach to model building. Phenomenological viability leads to a scenario with degenerate squark and slepton spectra and with heavy gauginos. Features of a Kähler potential that allows for such a scenario are described.
In a consistent top-down approach based on orbifold compactifications, modular and traditional flavor symmetries combine nontrivially to the so-called eclectic flavor symmetry. We extend this scheme from two extra dimensions, discussed previously, to the six extra dimensions of string theory. By doing so, new insights on the nature of CP and its spontaneous breaking emerge. Moreover, we identify a new interpretation of R-symmetries as unbroken remnants from modular symmetries that are associated with geometrically stabilized complex structure moduli. Hence, all symmetries (i.e. modular, tradit…
We study the origin of non-Abelian discrete flavor symmetries in superstring theory. We classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. These symmetries include D_4 and Delta(54). We find that the symmetries of the couplings are always larger than the symmetries of the compact space. This is because they are a consequence of the geometry of the orbifold combined with the space group selection rules of the string. We also study possible breaking patterns. Our analysis yields a simple geometric understanding of the realization of non-Ab…
The recent observations of atmospheric nu events from the Super-Kamiokande experiment are compatible with three-flavor neutrino oscillations, occurring dominantly in the nu_mu<--->nu_tau channel and subdominantly in the nu_mu<--->nu_e channel. We present an updated analysis of the three-flavor mass-mixing parameters consistent with the present phenomenology, including the latest 45 kTy data sample from Super-Kamiokande. A comparison with our previous results, based on 33 kTy data, shows that the oscillation evidence is strengthened, and that the neutrino mass-mixing parameters are constrained …
We investigate an effective flavor-symmetric Yang-Mills-Higgs model with $N^2-1$ adjoint scalar fields. We find a set of BPS equations that provide vortex solutions and calculate their energies for arbitrary representations. We show that, for a given N-ality $k$, the energy of the corresponding antisymmetric representation is the lowest. This completes the proof that this model is able to reproduce a Casimir law for the string tension at asymptotic distances.
We study the modular symmetry in magnetized D-brane models on $T^2$. Non-Abelian flavor symmetry $D_4$ in the model with magnetic flux $M=2$ (in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in heterotic orbifold models. The $T^2/Z_4$ orbifold model has the same modular symmetry as the magnetized brane model with $M=2$, and its flavor symmetry $D_4$ is a subgroup of the modular symmetry.
We examine a common origin of four-dimensional flavor, CP, and $U(1)_R$ symmetries in the context of heterotic string theory with standard embedding. We find that flavor and $U(1)_R$ symmetries are unified into the $Sp(2h+2, \mathbb{C})$ modular symmetries of Calabi-Yau threefolds with $h$ being the number of moduli fields. Together with the $\mathbb{Z}_2^{\rm CP}$ CP symmetry, they are enhanced to $GSp(2h+2, \mathbb{C})\simeq Sp(2h+2, \mathbb{C})\rtimes \mathbb{Z}_2^{\rm CP}$ generalized symplectic modular symmetry. We exemplify the $S_3, S_4, T^\prime, S_9$ non-Abelian flavor symmetries on e…
Delta(54) can serve as a flavor symmetry in particle physics, but remains almost unexplored. We show that in a classification of semi-realistic Z3xZ3 heterotic string orbifolds, Delta(54) turns out to be the most natural flavor symmetry, providing additional motivation for its study. We revisit its phenomenological potential from a low-energy perspective and subject to the constraints of string models. We find a model with Delta(54) arising from heterotic orbifolds that leads to the Gatto-Sartori-Tonin relation for quarks and charged-leptons. Additionally, in the neutrino sector, it leads to a…
A phenomenological approach for the universal mass matrix model with a broken flavor 2 <-> 3 symmetry is explored by introducing the 2 <-> 3 antisymmetric parts of mass matrices for quarks and charged leptons . We present explicit texture components of the matrices, which are consistent with all the neutrino oscillation experiments and quark mixing data. The mass matrices have a common structure for quarks and leptons, while the large lepton mixings and the small quark mixings are derived with no fine tuning due to the difference of the phase factors. The model predicts a value, 2.4 x 10^{-3},…
Eclectic flavor groups arising from string compactifications combine the power of modular and traditional flavor symmetries to address the flavor puzzle. This top-down scheme determines the representations and modular weights of all matter fields, imposing strict constraints on the structure of the effective potential, which result in controlled corrections. We study the lepton and quark flavor phenomenology of an explicit, potentially realistic example model based on a T6/Z3xZ3 orbifold compactification of the heterotic string that gives rise to an Omega(2) eclectic flavor symmetry. We find t…
We derive the potential modular symmetries of heterotic string theory. For a toroidal compactification with Wilson line modulus, we obtain the Siegel modular group $\mathrm{Sp}(4,\mathbb{Z})$ that includes the modular symmetries $\mathrm{SL}(2,\mathbb{Z})_T$ and $\mathrm{SL}(2,\mathbb{Z})_U$ (of the "geometric" moduli $T$ and $U$) as well as mirror symmetry. In addition, string theory provides a candidate for a CP-like symmetry that enhances the Siegel modular group to $\mathrm{GSp}(4,\mathbb{Z})$.
We present a calculating method for the quark and lepton mixing angles. After a general discussion in field theoretic models, we present a working model from a string compactification through $Z_{12-I}$ orbifold compactification. It is beyond presenting just three families of the standard model but is the first example from string compactification successfully fitting to the observed data. Assuming that all Yukawa couplings from string compactification are real, we also comment on a relation between the CP phases in the Jarlskog determinants obtained from the CKM and PMNS matrices. The flipped…
We investigate low energy implications of string loop corrections to supergravity couplings which break a possible flavor universality of the tree level. If Supersymmetry is broken by the dilaton $F$-term, universal soft scalar masses arise at the leading order but string loop corrections generically induce flavor-non-diagonal soft terms. Constraints from flavor changing neutral currents (FCNC) and CP violation then require a large supersymmtery breaking scale and thus heavy gluinos and squarks. If Supersymmetry is broken by moduli $F$-terms, universality at the string tree level can only be g…
We review the very stringent lower bounds on the string scale that arise from flavor considerations in models with intersecting branes. Despite the absence of a realistic flavor structure at tree level, flavor changing interactions induce a non-trivial pattern of fermion masses and mixing angles when quantum corrections are taken into account. The resulting realistic theory of flavor allows us to constrain, in an unambiguous way, the string scale up to levels difficult to reconcile non-supersymmetric models.
Stabilizing a heterotic string vacuum with a large expectation value of the dilaton and simultaneously breaking low-energy supersymmetry is a long-standing problem of string phenomenology. We reconsider these issues in light of the recent developments in F-theory.
We demonstrate that sizable neutrino flavor oscillations can be generated in a model with large extra spacetime dimensions even if the physics on the brane is flavor-diagonal, the bulk neutrino theory is flavor-neutral, and the brane/bulk couplings are flavor-blind. This is thus a compact model for addressing neutrino flavor oscillations in higher dimensions. We also discuss several phenomenological aspects of the ``bulk-mediated'' neutrino oscillations inherent in this model, and show that this model contains some potentially important new phenomenological features in the limit of large brane…
We devise minimalistic gauged U(1)_X Froggatt-Nielsen models which at low-energy give rise to the recently suggested discrete gauge Z_6 symmetry, proton hexality, thus stabilizing the proton. Assuming three generations of right-handed neutrinos, with the proper choice of X-charges, we obtain viable neutrino masses. Furthermore, we find scenarios such that no X-charged hidden sector superfields are needed, which from a bottom-up perspective allows the calculation of g_string, g_X and G_SM's Kac-Moody levels. The only mass scale apart from M_grav is m_soft.
A Z_2 orbifold compactification of the heterotic string is considered. The resulting 6D GUT groups can be SO(16) or E_7 times SU(2) plus some hidden sector groups. The N=4 supersymmetry is reduced to N=2. In particular, the SO(16) 6D model with one spinor representation 128 can reduce to the previous 5D SO(16) or SO(14) family unification models after compactifying the sixth dimension. To obtain one spinor, we have to take into account the left-over center of SO(16). We also comment on the E_7 times SU(2) model.
We study some phenomenological consequences of having moduli fields with large vacuum expectation values (v.e.v.). The v.e.vs of the moduli are dynamically determined once supersymmetry is broken in 4D string theories. The study constraints the possible Yukawa interactions and modular weights for matter fields.
We consider extensions of the standard model inspired by intersecting D-brane constructions, in order to address flavor mass textures. We include additional anomalous gauge symmetries, and scalar fields to break them and to generate Froggatt-Nielsen mass terms. Green-Schwarz axions are included to cancel mixed anomalies rendering the models consistent. At low energies, a residual anomalous global symmetry remains, and its associated pseudo-Goldstone mode becomes the physical axion, which can be interpreted as an axion arising from open string modes. General considerations show that such axions…
We report some recent progress towards classification of phenomenologically appealing heterotic string models in the Free Fermionic Formulation. We focus on a class of Z2xZ2 models with SO(10) space-time gauge symmetry and study their main phenomenological aspects. We further consider reducing the gauge symmetry to the Pati-Salam gauge group SU(4)XSU(2)_LxSU(2)_R and impose a series of phenomenological constraints including the existence of gauge symmetry breaking Higgs particles and the elimination of exotic fractionally charged states.
This article is the PhD thesis of the author. It is focused on Type II compactifications because of the potential for the construction of realistic MSSM-like compactifications. In particular we concentrate in Type IIB Calabi-Yau orientifolds and its non-perturbative realization: F-theory. These sort of models, have attracted a lot of attention during recent years due to their phenomenological interest. The first part is devoted to an introductory survey of some concepts and aspects of Type II vacua like e.g. the low energy effective action or soft terms. It is also included a brief presentatio…
In a QCD-like string model based on D6 flavor branes in the presence of D4 color branes wrapping one of the compactified dimension on an $S^1$, the shape of meson strings in the five dimensional curved space as well as the potential between quark and anti-quark are investigated. The flavor branes on which both ends of a meson string live are assumed to be separated in this five dimensional space, depending on the values of the constituent quark masses. It is shown in this picture that the meson string with different flavors on both ends changes its shape at a critical distance. There is, howev…
The Standard Model is the low-energy limit of a microscopic theory which includes extra dimensions and new symmetries. A part of my thesis consisted in constructing a new class of models with two extra dimensions. We showed that these models can drive a dynamical symmetry breaking in four dimensions. In particular, they are dual to models with four fermions which need a non-perturbative treatment. We also studied supersymmetry and its local version, supergravity, in string theory inspired models with ten dimensions. Extra fields called moduli are present after dimensional reduction and are gen…
We investigate the phenomenology of an orbifold string model in which supersymmetry breaking is dominated by the overall `size' modulus field and all matter fields are in the untwisted sector. The possibly close degeneracy of the lightest neutralino and chargino and the possibly small splitting between the gluino and chargino/LSP mass imply that discovery of supersymmetry at future colliders could be more challenging than anticipated. Specialized search strategies and particular detector features could play an important role. For preferred model parameter choices, the phenomenology of dark mat…
We present a class of supersymmetric models in which symmetry considerations alone dictate the form of the soft SUSY breaking Lagrangian. We develop a class of minimal models, denoted as sMSSM -- for flavor symmetry-based minimal supersymmetric standard model, which respect a grand unified symmetry such as SO(10) and a non-Abelian flavor symmetry H which suppresses SUSY-induced flavor violation. Explicit examples are constructed with the flavor symmetry being gauged SU(2)_H and SO(3)_H with the three families transforming as 2 + 1 and 3 representations respectively. A simple solution is found …
We discuss a supersymmetric model with discrete flavor symmetry $A_4\times Z_3$. The additional scalar fields which contribute masses of leptons in the Yukawa terms are introduced in this model. We analyze their scalar potential and find that they have various vacuum structures. We show the relations among 24 different vacua and classify them into two types. We derive expressions of the lepton mixing angles, Dirac CP violating phase and Majorana phases for the two types. The model parameters which are allowed by the experimental data of the lepton mixing angles are different for each type. We …
We investigate a gauge theory realization of non-Abelian discrete flavor symmetries and apply the gauge enhancement mechanism in heterotic orbifold models to field-theoretical model building. Several phenomenologically interesting non-Abelian discrete symmetries are realized effectively from a $U(1)$ gauge theory with a permutation symmetry. We also construct a concrete model for the lepton sector based on a $U(1)^2 \rtimes S_3$ symmetry.
Using phenomenological formulae, we deduce the masses and quantum numbers of the quarks from two elementary quarks ($ε_{u}$ and $ε_{d}$) first. Then using the sum laws and a binding energy formula, in terms of the qqq baryon model and SU(4), we deduce the masses and quantum numbers of the important baryons from the deduced quarks. At the same time, using the sum laws and a binding energy formula, in terms of the quark-antiquark bound state meson model, we deduce the masses and quantum numbers of the mesons from the deduced quarks. The deduced masses of the baryons and mesons are 98% consistent…
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…
Flavor symmetry plays a crucial role in the standard model of particle physics but its origin is still unknown. We develop a new method (based on outer automorphisms of the Narain space group) to determine flavor symmetries within compactified string theory. A picture emerges where traditional (discrete) flavor symmetries, CP-like symmetries and modular symmetries (like T-duality) of string theory combine to unified flavor symmetries. The groups depend on the geometry of compact space and the geographical location of fields in the extra dimensions. We observe a phenomenon of "local flavor grou…
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…
We calculate the soft SUSY breaking terms arising from a large class of string scenarios, namely symmetric orbifold constructions, and study its phenomenological viability. They exhibit a certain lack of universality, unlike the usual assumptions of the minimal supersymmetric standard model. Assuming gaugino condensation in the hidden sector as the source of SUSY breaking, it turns out that squark and slepton masses tend to be much larger than gaugino masses. Furthermore, we show that these soft breaking terms can be perfectly consistent with both experimental and naturalness constraints (the …
We investigate the interplay between the string scale and phenomenological scales in orientifold compactifications. Specifically, we discuss in generality the tension that often arises in accounting for neutrino masses, Yukawa couplings, and a mu-term of the correct order and show that it often constrains the string scale M_s. The discussion focuses on two scenarios where, (1) the observed order of the neutrino masses are accounted for by a D-instanton induced "stringy" Weinberg operator, or (2) effectively via the type I seesaw mechanism with an instanton induced Majorana mass term. In both s…
We study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion mass hierarchies and sizable CP-breaking effects. We investigate whether one can dynamically fix the moduli values in the vicinity of the fixed points in the context of Type IIB string theory. It is found that the string landscape prefers $|δτ| \simeq 10^{-5}$ for the deviation of the complex structure modulus from all fixed points and the CP-breaking vacuum is…
Warped 5-dimensional models, based on the original Randall-Sundrum geometry, have been extended beyond their initial purpose of resolving the gauge hierarchy problem. Over the past decade, various ingredients have been added to their basic structure in order to provide natural and predictive models of flavor and also to address existing constraints from precision data. In this review, we examine the theoretical and experimental status of realistic models that accommodate current data, while addressing the hierarchy and flavor puzzles of the Standard Model. We also discuss the prospects for fut…
We argue that in large classes of string compactifications with a MSSM-like structure substantial flavor violating SUSY-breaking soft terms are generically induced. We specify to the case of flavor dependent soft-terms in type IIB/F-theory SU(5) unified models, although our results can be easily extended to other settings. The Standard Model (SM) degrees of freedom reside in a local system of 7-branes wrapping a 4-fold S in the extra dimensions. It is known that in the presence of closed string 3-form fluxes SUSY-breaking terms are typically generated. We explore the generation dependence of t…
For the weakly coupled heterotic string (WCHS) there is a well-known factor of twenty conflict between the minimum string coupling unification scale, Lambda_H ~5x10^(17) GeV, and the projected MSSM unification scale, Lambda_U ~ 2.5x10^(16) GeV, assuming an intermediate scale desert (ISD). Renormalization effects of intermediate scale MSSM-charged exotics (ISME) (endemic to quasi-realistic string models) can resolve this issue, pushing the MSSM scale up to the string scale. However, for a generic string model, this implies that the projected Lambda_U unification under ISD is accidental. If the …
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 requi…
Motivated by the fact that the string scale can be many orders of magnitude lower than the Planck mass, we investigate the required modifications in the MSSM $β$--functions in order to achieve intermediate ($10^{10-13}$GeV) scale unification, keeping the traditional logarithmic running of the gauge couplings. We present examples of string unified models with the required extra matter for such a unification while we also check whether other MSSM properties (such as radiative symmetry breaking) are still applicable.
We correct our treatment of decays of the lightest chargino to final states containing the lightest neutralino in the case where the chargino and neutralino masses differ by less than 1 GeV. A brief summary of the phenomenological implications is given.
We propose a third idea for the explanation of the leptonic flavor structure in addition to the prominent approaches based on flavor symmetry and anarchy. Typical flavor patterns can be modeled by using mass spectra obtained from the discrete lengths spectrum of tight knots and links. We assume that a string theory model exists in which this idea can be incorporated via the Majorana mass structure of a type I seesaw model. It is shown by a scan over the parameter space that such a model is able to provide an excellent fit to current neutrino data and that it predicts a normal neutrino mass hie…
We analyse the phenomenological viability of heterotic $Z_3$ orbifold models with two Wilson lines, which naturally predict three families of matter and Higgs fields. We study the orbifold parameter space, and discuss the compatibility of the predicted Yukawa couplings with current experimental data, thus evaluating the viability of the orbifold configurations. We address the implications of tree-level flavour changing neutral processes in constraining the Higgs sector of the model, finding that viable scenarios can be obtained for a fairly light Higgs spectrum.
There are theoretical and phenomenological motivations that there may exist additional heavy Z' bosons with family non-universal couplings. Flavor mixing in the quark and lepton sectors will then lead to flavor changing couplings of the heavy Z', and also of the ordinary Z when Z-Z' mixing is included. The general formalism of such effects is described, and applications are made to a variety of flavor changing and CP-violating tree and loop processes. Results are described for three specific cases motivated by a specific heterotic string model and by phenomenological considerations, including …
Soft supersymmetry breaking terms were recently derived for type IIB string flux compactifications with all moduli stabilised. Depending on the choice of the discrete input parameters of the compactification such as fluxes and ranks of hidden gauge groups, the string scale was found to have any value between the TeV and GUT scales. We study the phenomenological implications of these compactifications at low energy. Three realistic scenarios can be identified depending on whether the Standard Model lies on D3 or D7 branes and on the value of the string scale. For the MSSM on D7 branes and the s…
