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Register a new userMonodromic T-Branes And The $SO(10)_{GUT}$
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Johar M. Ashfaque
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T-branes, which are non-Abelian bound states of branes, were first introduced by Cecotti, Cordova, Heckman and Vafa cite{Cecotti:2010bp}. They are the refined version of the monodromic branes that feature in the phenomenological F-theory models. Here, we will be interested in the T-brane corresponding to the $Z_3$ monodromy which is used to break the $E_8$ gauge group to obtain the $SO(10)_{GUT}$. This extends the results of cite{Cecotti:2010bp} to the case of $Z_3$ monodromic T-branes used to break the $E_8$ gauge group to $SO(10)times SU(3)times U(1)$ and compute the Yukawa coupling with the help of the residue formula. We conclude that the Yukawa coupling, ${bf{10}}_{H}cdot {bf{16}}_{M}cdot {bf{16}}_{M}$, is non-zero for $E_7$, in complete agreement with cite{Cecotti:2010bp}, but is zero for $E_8$. Furthermore, the case of $Z_2$ monodromic T-branes used to break the $E_8$ gauge group to $E_{6}times SU(2)times U(1)$, nothing interesting can be deduced by evaluating the Yukawa coupling ${bf{27}}_{H}cdot {bf{27}}_{M}cdot {bf{27}}_{M}$ which is dependent on whether the MSSM fermion and electroweak Higgs fields can be included in the same ${bf{27}}$ multiplet of a three-family $E_6$ GUT or assign the Higgs fields to a different ${bf{27}}_{H}$ multiplet where only the Higgs doublets and singlets obtain the electroweak scale energy.
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The clockwork mechanism, which can naturally explain the origin of small numbers, is implemented in $SO(10)$ grand unified theories to address the origin of hierarchies in fermion masses and mixings. We show that a minimal Yukawa sector involving a $10_H$ and $overline{126}_H$ of Higgs bosons, extended with two clockwork chains consisting of $16+overline{16}$ vector-like fermions, can explain the hierarchical patterns with all the Yukawa couplings being of order one. Emergence of a realistic mass spectrum does not require any symmetry that distinguishes the three generations. We develop clockwork-extended $SO(10)$ GUTs both in the context of SUSY and non-SUSY frameworks. Implementation of the mechanism in non-SUSY scenario assumes a Peccei-Quinn symmetry realized at an intermediate scale, with the clockwork sector carrying non-trivial charges, which solves the strong CP problem and provides axion as a dark matter candidate.
SO(10) GUT models with only small Higgs fields use higher-dimensional operators to generate realistic fermion mass matrices. In particular, a Higgs field in the spinor representation, 16^d_H, acquires a weak scale vev. We include the weak vev of the corresponding field bar{16}^u_H and investigate the effect on two successful models, one by Albright and Barr (AB) and another by Babu, Pati and Wilczek (BPW). We find that the BPW model is a particular case within a class of models with identical fermion masses and mixings. In contrast, we expect corrections to the parameters of AB-type models.
Supersymmetric GUTs based on SO(10) gauge group are leading contenders to describe particle physics beyond the Standard Model. Among these the New minimal supersymmetric SO(10) grand unified theory (NMSGUT) based on Higgs system 10+120+210+126+$overline{126}$ has been developing since 1982. It now successfully fits the whole standard Model gauge coupling, symmetry breaking and fermion mass-mixing data as well as the neutrino mass and mixing data in terms of NMSGUT parameters and just 6 soft supersymmetry breaking parameters defined at the GUT scale. In this thesis we study the phenomenology of NMSGUT, its implications for inflationary and Cold Dark matter cosmology and develop Renormalization group(RG) equations for the flow of NMSGUT couplings in the extreme ultraviolet. In the first part we show that superheavy threshold effects can drastically lower the SO(10) yukawa couplings required for realistic unification and this cures the long standing problem of fast proton decay in Susy GUT. Then we propose a novel Supersymmetric Seesaw inflection(SSI) scenario based upon a SU(2)_L x U(1)_R x U(1)_{B-L} invariant model, where the inflation mass is controlled by the large conjugate sneutrino mass. We show that it is much less fine-tuned and more stable than Dirac sneutrino based MSSM inflation. NMSGUT can embed SSI, and even provide a large tensor scalar ratio, but obstacles in achieving enough inflation remain. The NMSGUT Bino LSP is a good dark matter candidate when it can co-annihilate with a nearly degenerate sfermion as in fits with a light smuon. We also calculate two loop NMSGUT gauge-Yukawa Renormalization Group(RG) beta functions and show that GUT scale negative Higgs mass squared parameters required by NMSGUT fits can arise by RG flows from positive values at the Planck scale.
The Supersymmetric SO(10) theory (NMSO(10)GUT) based on thehfilbreak ${bf{210+126 +oot}}$ Higgs system proposed in 1982 has evolved into a realistic theory capable of fitting the known low energy Particle Physics data besides providing a Dark matter candidate and embedding Inflationary Cosmology. It dynamically resolves longstanding issues such as fast dimension five operator mediated proton decay in Susy GUTs by allowing explicit and complete calculation of crucial threshold effects at $M_{Susy}$ and $M_{GUT}$ in terms of fundamental parameters. This shows that SO(10) Yukawas responsible for observed fermion masses as well as operator dimension 5 mediated proton decay can be highly suppressed on a Higgs dissolution edge in the parameter space of GUTs with rich superheavy spectra. This novel and generically relevant result highlights the need for every realistic UV completion model with a large/infinite number of heavy fields coupled to the light Higgs doublets to explicitly account for the large wave function renormalization effects on emergent light Higgs fields in order to be considered a quantitatively well defined candidate UV completion. The NMSGUT predicts large soft Susy breaking trilinear couplings and distinctive sparticle spectra. Measurable or near measurable level of tensor perturbations- and thus large Inflaton mass scale- may be accommodated by Supersymetric Seesaw inflation within the NMSGUT based on an LHN flat direction Inflaton if the Higgs component contains contributions from heavy Higgs components. Successful NMSGUT fits suggest a emph{renormalizable} Yukawon Ultra minimal gauged theory of flavor based upon the NMSGUT Higgs structure.
Supersymmetric $SO(10)$ grand unified models with renormalizable Yukawa couplings involving only ${bf 10}$ and $overline{bf 126}$ Higgs fields have been shown to realize the fermion masses and mixings economically. In previous works, the sum rule of the fermion mass matrices are given by inputting the quark matrices, and the neutrino mixings are predicted in this framework. Now the three neutrino mixings have been measured, and in this paper, we give the sum rule by inputting the lepton mass matrices, which makes clear certain features of the solution, especially if the vacuum expectation values of ${bf 126}+ overline{bf126}$ ($v_R$) are large and the right-handed neutrinos are heavy. We perform the $chi^2$ analyses to fit the fermion masses and mixings using the sum rule. In previous works, the best fit appears at $v_R sim 10^{13}$ GeV, and the fit at the large $v_R$ scale ($sim 10^{16}$ GeV) has been less investigated. Our expression of the sum rule has a benefit to understand the flavor structure in the large $v_R$ solution. Using the fit results, we perform the calculation of the $mu to egamma$ process and the electric dipole moment of electron, and the importance of $v_R$ dependence emerges in low energy phenomena. We also show the prediction of the CP phase in the neutrino oscillations, which can be tested in the near future.
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