Vectorlike Particles, Z′Z' and Yukawa Unification in F-theory inspired E6E_6

We explore the low energy implications of an F-theory inspired $E_6$ model whose breaking yields, in addition to the MSSM gauge symmetry, a $Z'$ gauge boson associated with a $U(1)$ symmetry broken at the TeV scale. The zero mode spectrum of the effective low energy theory is derived from the decomposition of the $27$ and $\overline{27}$ representations of $E_6$ and we parametrise their multiplicities in terms of a minimum number of flux parameters. We perform a two-loop renormalisation group analysis of the gauge and Yukawa couplings of the effective theory model and estimate lower bounds on the new vectorlike particles predicted in the model. We compute the third generation Yukawa couplings in an F-theory context assuming an $E_8$ point of enhancement and express our results in terms of the local flux densities associated with the gauge symmetry breaking. We find that their values are compatible with the ones computed by the renormalisation group equations, and we identify points in the parameter space of the flux densities where the $t-b-\tau$ Yukawa couplings unify.Comment: 16 pages, revised version to appear in PL

750 GeV Diphoton excess from E6E_6 in F-theory GUTs

We interpret the 750-760 GeV diphoton resonance as one or more of the spinless components of a singlet superfield arising from the three 27-dimensional representations of $E_6$ in F-theory, which also contain three copies of colour-triplet charge $\mp 1/3$ vector-like fermions $D_i,\bar{D}_i$ and inert Higgs doublets to which the singlets may couple. For definiteness we consider (without change) a model that was proposed some time ago which contains such states, as well as bulk exotics, leading to gauge coupling unification. The smoking gun prediction of the model is the existence of other similar spinless resonances, possibly close in mass to 750-760 GeV, decaying into diphotons, as well as the three families of vector-like fermions $D_i,\bar{D}_i$.Comment: 15 pages, 5 figures, minor corrections, reference

R-Parity violation in F-Theory

We discuss R-parity violation (RPV) in semi-local and local F-theory constructions. We first present a detailed analysis of all possible combinations of RPV operators arising from semi-local F-theory spectral cover constructions, assuming an $SU(5)$ GUT. We provide a classification of all possible allowed combinations of RPV operators originating from operators of the form $10\cdot \bar 5\cdot \bar 5$, including the effect of $U(1)$ fluxes with global restrictions. We then relax the global constraints and perform explicit computations of the bottom/tau and RPV Yukawa couplings, at an $SO(12)$ local point of enhancement in the presence of general fluxes subject only to local flux restrictions. We compare our results to the experimental limits on each allowed RPV operator, and show that operators such as $LLe^c$, $LQd^c$ and $u^cd^cd^c$ may be present separately within current bounds, possibly on the edge of observability, suggesting lepton number violation or neutron-antineutron oscillations could constrain F-theory models.Comment: 40 pages, 13 figures, minor correction

MSSM from F-theory SU(5) with Klein Monodromy

We revisit a class of $SU(5)$ SUSY GUT models which arise in the context of the spectral cover with Klein Group monodromy $V_4=Z_2\times Z_2$. We show that $Z_2$ matter parities can be realised via new geometric symmetries respected by the spectral cover. We discuss a particular example of this kind, where the low energy effective theory below the GUT scale is just the MSSM with no exotics and standard matter parity, extended by the seesaw mechanism with two right-handed neutrinos

Construction and phenomenological analysis of GUTs in superstring and D-brane theories

In this thesis, we present string theory models and we study their phenomenological consequences.We focus on the non-perturbative version of type IIB superstring theory, known as F-theory, where non-Abelian gauge symmetries are linked to the singularities of the elliptically fibred compactification manifold. These singularities are of the ADE type and as a result the E8exceptional group is the highest one. Hence, popular grand unified theories (GUTs) based on thegroups E6, SO(10) and SU(5), can be naturally realised as effective F-theory models. Withinthis framework we derive and study the low energy implications of several models. Firstly, anF-theory supersymmetric SU(5) model accompanied by V4 Klein monodromy and a Z2 geometricparity is derived. At low energies, the model leads to the MSSM spectrum extended by tworight-handed neutrinos seesaw mechanism. Next,a model based on SU(5), together with thenon-Abelian family symmetry D4 plus an Abelian family symmetry is presented. The modelproduces a realistic low energy spectrum and is capable to explain the neutrino mixing effectspredicted by neutrino oscillation experiments. Due to a Z2 geometric parity the model is shownto exhibit baryon violating processes, without proton decay. A systematic study on R-parityviolation (RPV) effects in semi-local and local F-theory constructions follows, where we haveshown that RPV is a generic feature, but may occur without proton decay, due to flux effects.The values of RPV Yukawa couplings are also computed in an F-theory local background andcompared with their corresponding values from field theory results. Next, we explore the low energyimplications of F-theory inspired E6 models, in which a light Z’ neutral gauge boson survives at low energies. The breaking to SO(10) and then to SU(5) is performed with the help of Abelian fluxes. The low-energy spectrum is then chosen to be part of this high-energy spectrum and consists of MSSM plus some vectorlike exotics. A renormalisation group analysis at two-loop level for gauge and Yukawa couplings is performed and it is shown to be compatible with the high-energy predictions coming from the computation of Yukawa couplings in F-theory. We also identify points in the parameter space of the flux densities where the top, bottom and tau Yukawa couplings unify.Η παρούσα διατριβή διαπραγματεύεται την κατασκευή και μελέτη των χαμηλοενεργειακών επιπτώσεων διάφορων μοντέλων που προκύπτουν από το πλαίσιο της θεωρίας υπερχορδών και συγκεκριμένα από τη 12-διάστατη εκδοχή της θεωρίας τύπου-ΙΙΒ, γνωστή και ως θεωρία-F. Αρχικά, παρουσιάζεται ένα υπερσυμμετρικό μοντέλο SU(5) το οποίο συνοδεύεται από μία Klein V4 monodromy καθώς και μία Z2 parity γεωμετρικής προέλευσης. Στις χαμηλές ενέργειες, το σωματιδιακό φάσμα του μοντέλου ταυτίζεται με αυτό του MSSM εκτετάμενο από δύο δεξιόστροφα νετρίνο. Στη συνέχεια, μελετάτε ένα SU(5) μοντέλο το οποίο αυτή τη φορά συνοδεύεται από την μη-Αβελιανή διακριτή συμμετρία D4 και έναν Αβελιανό παράγoντα U(1). Στις χαμηλές ενέργειες το μοντέλο προβλέπει ένα ρεαλιστικό φάσμα σωματιδιακών καταστάσεων και είναι ικανό να ερμηνεύσει τα φαινόμενα ανάμιξης των νετρίνων όπως αυτά προκύπτουν από τα πειραματικά δεδομένα. Επιπλέον, λόγω της ύπαρξης μίας γεωμετρικής Z2 parity, το μοντέλο προβλέπει διαδικασίες παραβίασης του βαρυονικού αριθμού όπως ταλαντώσεις νετρονίου-αντινετρονίου, ενώ ταυτόχρονα απουσιάζουν αθέμιτα φαινόμενα διάσπασης πρωτονίου. Aκολουθεί μία συστηματική μελέτη φαινομένων παραβίασης της R-parity στην ημι-τοπική και τοπική προσέγγιση της θεωρίας-F, από την οποία προκύπτει ότι τα φαινόμενα αυτά αποτελούν γενικό χαρακτηριστικό της θεωρίας, μπορούν όμως να υπάρχουν χωρίς φαινόμενα διάσπασης του πρωτονίου λόγω της ύπαρξης μαγνητικών ροών. Επιπλέον, οι τιμές των συντελεστών σύζευξης Yukawa των όρων παραβίασης της R-parity υπολογίζονται στην τοπική προσέγγιση της θεωρίας-F και συγκρίνονται με τις αντίστοιχες τιμές που προκύπτουν από την θεωρία πεδίου. Τέλος, γίνεται μελέτη E6 μοντέλων από τη θεωρία-F, τα οποία προβλέπουν την ύπαρξη ενός ελαφριού μποζονίου βαθμίδας Z' στις χαμηλές ενέργειες. Η ρήξη της συμμετρίας E6 στην SO(10) και έπειτα στην SU(5) επιτυγχάνεται μέσω Αβελιανών μαγνητικών ροών. Το σωματιδιακό φάσμα των μοντέλων αποτελείται από το MSSM και επιπλέον διανυσματικού τύπου εξωτικές καταστάσεις. Πραγματοποιείται ανάλυση της ομάδας εξισώσεων ανακανονικοποίησης σε επίπεδο δύο-βρόγχων για τους συντελεστές σύζευξης βαθμίδας και Yukawa και δείχνεται ότι στις υψηλές ενέργειες τα αποτελέσματα είναι συγκρίσιμα με τις προβλέψεις που προέρχονται από τον υπολογισμό συντελεστών σύζευξης Yukawa στην θεωρία-F. Τέλος, προσδιορίζονται σημεία του παραμετρικού χώρου της θεωρίας όπου οι συντελεστές Yukawa των φερμιονίων top, bottom και tau ενοποιούνται

Smooth hybrid inflation with low reheat temperature and observable gravity waves in SU(5) × U(1)χ_{χ} super-GUT

We realize smooth hybrid inflation in the framework of supersymmetric SU(5) × U(1)$_{χ}$ ⊂ SO(10) model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of SU(5). The breaking of U(1)$_{χ}$ symmetry leaves a residual discrete Z $_{2}$ symmetry, that serves as the MSSM matter parity, realizing the possibility of the lightest supersymmetric particle as a cold dark matter candidate. The d = 5 proton lifetime for the decay p ⟶ K $^{+}$ν̅, mediated by color-triplet Higgsinos is found to satisfy current experimental bounds if split-high scale SUSY scenario is employed. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital rôle in bringing the scalar spectral index ns within the Planck's latest bounds. In a minimal Kähler potential setup, small values of tensor-to-scalar ratio r ≲ 3.5 × 10$^{-7}$ are obtained, whereas the gravitino mass turns out to be in the range that favors PeV scale SUSY but is not sufficiently high to avoid the d = 5 proton decay. A non-minimal Kähler potential including higher order corrections is required to realize successful inflation with central value of scalar spectral index ns = 0.9655, large tensor modes r ≲ 0.056 and a low reheat temperature (3 × 10$^{6}$ ≲ Tr ≲ 6.5 × 10$^{7}$) GeV consistent with leptogenesis and baryogenesis.We realize smooth hybrid inflation in the framework of supersymmetric $SU(5) \times U(1)_{\chi}\subset SO(10)$ model which provides a natural solution to the monopole problem appearing in the spontaneous symmetry breaking of $SU(5)$. The breaking of $U(1)_{\chi}$ symmetry leaves a residual discrete $Z_2$ symmetry, that serves as the MSSM matter parity, realizing the possibility of the lightest supersymmetric particle as a cold dark matter candidate. The $d = 5$ proton lifetime for the decay $p \rightarrow K^+ \bar{\nu}$, mediated by color-triplet Higgsinos is found to satisfy current experimental bounds if split-high scale SUSY scenario is employed. We show that with minimal Kähler potential, the soft supersymmetry breaking terms play a vital rôle in bringing the scalar spectral index $n_s$ within the Planck's latest bounds. In a minimal Kähler potential setup, small values of tensor-to-scalar ratio $r \lesssim 3.5 \times 10^{-7}$ are obtained, whereas the gravitino mass turns out to be in the range that favors PeV scale SUSY but is not sufficiently high to avoid the $d = 5$ proton decay. A non-minimal Kähler potential including higher-order corrections is required to realize successful inflation with central value of scalar spectral index $n_s = 0.9655$, large tensor modes $r \lesssim 0.056$ and a low reheat temperature $(3\times 10^{6} \lesssim T_r \lesssim 6.5 \times 10^7 )$ GeV consistent with leptogenesis and baryogenesis

Discrete Family Symmetry from F-Theory GUTs

We consider realistic F-theory GUT models based on discrete family symmetries $A_4$ and $S_3$, combined with $SU(5)$ GUT, comparing our results to existing field theory models based on these groups. We provide an explicit calculation to support the emergence of the family symmetry from the discrete monodromies arising in F-theory. We work within the spectral cover picture where in the present context the discrete symmetries are associated to monodromies among the roots of a five degree polynomial and hence constitute a subgroup of the $S_5$ permutation symmetry. We focus on the cases of $A_4$ and $S_3$ subgroups, motivated by successful phenomenological models interpreting the fermion mass hierarchy and in particular the neutrino data. More precisely, we study the implications on the effective field theories by analysing the relevant discriminants and the topological properties of the polynomial coefficients, while we propose a discrete version of the doublet-triplet splitting mechanism