A brane-world $SU(5)$ GUT model with global non-Abelian vortices is constructed in six-dimensional spacetime. We find a solution with a vortex associated to $SU(3)$ separated from another vortex associated to $SU(2)$. This $3-2$ split configuration a
chieves a geometric Higgs mechanism for $SU(5)to SU(3)times SU(2)times U(1)$ symmetry breaking. A simple deformation potential induces a domain wall between non-Abelian vortices, leading to a linear confining potential. The confinement stabilizes the vortex separation moduli, and assures the vorticity of $SU(3)$ group and of $SU(2)$ group to be identical. This dictates the equality of the numbers of fermion zero modes in the fundamental representation of $SU(3)$ (quarks) and of $SU(2)$ (leptons), leading to quark-lepton generations. The standard model massless gauge fields are localized on the non-Abelian vortices thanks to a field-dependent gauge kinetic function. We perform fluctuation analysis with an appropriate gauge fixing and obtain a four-dimensional effective Lagrangian of unbroken and broken gauge fields at quadratic order. We find that $SU(3) times SU(2) times U(1)$ gauge fields are localized on the vortices and exactly massless. Complications in analyzing the spectra of gauge fields with the nontrivial gauge kinetic function are neatly worked out by a vector-analysis like method.
Supersymmetric (SUSY) extension of the Standard Model (SM) is a primary candidate for new physics beyond the SM. If SUSY breaking scale is very low, for example, the multi-TeV range, and the SUSY breaking sector, except for the goldstino (gravitino),
is decoupled from the low energy spectrum, the hidden sector effect in the minimal SUSY SM (MSSM) is well described by employing the goldstino chiral superfield ($X$) with the nilpotent condition of $X^2=0$. Although this so-called nonlinear MSSM (NL-MSSM) provides a variety of interesting phenomenologies, there is a cosmological problem that the lightest superpartner gravitino is too light to be the major component of the dark matter (DM) in our universe. To solve this problem, we propose a minimal extension of the NL-MSSM by introducing a parity-odd SM singlet chiral superfield ($Phi$). We show that the interaction of the scalar component in $Phi$ with the MSSM Higgs doublets is induced after eliminating F-component of the goldstino superfield and the lightest real scalar in $Phi$ plays the role of the Higgs-portal DM. With a suitable choice of the model parameters, a successful Higgs-portal DM scenario can be realized while achieving the SM-like Higgs boson mass of 125 GeV from the tree-level Higgs potential through the multi-TeV SUSY breaking effect.
It is important to obtain (nearly) massless localized modes for the low-energy four-dimensional effective field theory in the brane-world scenario. We propose a mechanism for bosonic zero modes using the field-dependent kinetic function in the classi
cal field theory set-up. As a particularly simple case, we consider a domain wall in five dimensions, and show that massless states for scalar (0-form), vector (1-form), and tensor (2-form) fields appear on a domain wall, which may be called topological because of robustness of their existence (insensitive to continuous deformations of parameters). The spin of localized massless bosons is selected by the shape of the nonlinear kinetic function, analogously to the chirality selection of fermion by the well-known Jackiw-Rebbi mechanism. Several explicitly solvable examples are given. We consider not only (anti)BPS domain walls in non-compact extra dimension but also non-BPS domain walls in compact extra dimension.
We study vacua and walls of mass-deformed Kahler nonlinear sigma models on $Sp(N)/U(N)$. We identify elementary walls with the simple roots of $USp(2N)$ and discuss compressed walls, penetrable walls and multiwalls by using the moduli matrix formalism.
We propose a minimal and self-contained model in non-compact flat five dimensions which localizes the Standard Model (SM) on a domain wall. Localization of gauge fields is achieved by the condensation of Higgs field via a Higgs dependent gauge kineti
c term in five-dimensional Lagrangian. The domain wall connecting vacua with unbroken gauge symmetry drives the Higgs condensation which provides both electroweak symmetry breaking and gauge field localization at the same time. Our model predicts higher-dimensional interactions $|H|^{2n}(F_{mu u})^2$ in the low-energy effective theory. This leads to two expectations: The one is a new tree-level contribution to $H to gammagamma$ ($H to gg$) decay whose signature is testable in future LHC experiment. The other is a finite electroweak monopole which may be accessible to the MoEDAL experiment. Interactions of translational Nambu-Goldstone boson is shown to satisfy a low-energy theorem.
Dynamical localization of non-Abelian gauge fields in non-compact flat $D$ dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a situation typica
lly arises in the presence of topological solitons. We construct four-dimensional low-energy effective Lagrangian up to the quadratic order in a universal manner applicable to any spacetime dimensions. We devise an extension of the $R_xi$ gauge to separate physical and unphysical modes clearly. Out of the D-dimensional non-Abelian gauge fields, the physical massless modes reside only in the four-dimensional components, whereas they are absent in the extra-dimensional components. The universality of non-Abelian gauge charges holds due to the unbroken four-dimensional gauge invariance. We illustrate our methods with models in $D=5$ (domain walls), in $D=6$ (vortices), and in $D=7$.
We construct examples of cohomogeneity one special Lagrangian submanifolds in the cotangent bundle over the complex projective space, whose Calabi-Yau structure was given by Stenzel. For each example, we describe the condition of special Lagrangian a
s an ordinary differential equation. Our method is based on a moment map technique and the classification of cohomogeneity one actions on the complex projective space classified by Takagi.
Combining the semi-classical localization mechanism for gauge fields with $N$ domain wall background in a simple $SU(N)$ gauge theory in five space-time dimensions we investigate the geometric Higgs mechanism, where a spontaneous breakdown of the gau
ge symmetry comes from splitting of domain walls. The mass spectra are investigated in detail for the phenomenologically interesting case $SU(5) to SU(3)times SU(2)times U(1)$ which is realized on a split configuration of coincident triplet and doublet of domain walls. We derive a low energy effective theory in a generic background using the moduli approximation, where all non-linear interactions between effective fields are captured up to two derivatives. We observe novel similarities between domain walls in our model and D-branes in superstring theories.
We present a field theoretical model unifying grand unified theory (GUT) and brane world scenario. As a concrete example, we consider $SU(5)$ GUT in 4+1 dimensions where our 3+1 dimensional spacetime spontaneously arises on five domain walls. A field
-dependent gauge kinetic term is used to localize massless non-Abelian gauge fields on the domain walls and to assure the charge universality of matter fields. We find the domain walls with the symmetry breaking $SU(5)to SU(3)times SU(2)times U(1)$ as a global minimum and all the undesirable moduli are stabilized with the mass scale of $M_{rm GUT}$. Profiles of massless Standard Model particles are determined as a consequence of wall dynamics. The proton decay can be exponentially suppressed.
Thermal inflation driven by a scalar field called flaton is a possible scenario to solve the cosmological moduli problem. We study a model of thermal inflation with a flaton chemical potential. In the presence of the chemical potential, a negative ma
ss squared of the flaton, which is necessary to terminate the thermal inflation, is naturally induced. We identify the allowed parameter region for the chemical potential ($mu$) and the flaton self-coupling constant to solve the cosmological moduli problem and satisfy theoretical consistencies. In general, the chemical potential is a free parameter and it can be taken to be much larger than the typical scale of soft supersymmetry breaking parameters of $mathcal{O} (1)$ TeV. For $mu gtrsim 10^8$ GeV, we find that the reheating temperature after the thermal inflation can be high enough for the thermal leptogenesis scenario to be operative. This is in sharp contrast to the standard thermal inflation scenario, in which the reheating temperature is quite low and a special mechanism is necessary for generating sufficient amount of baryon asymmetry in the Universe after thermal inflation.
