The exact decomposition of gauge variables in lattice Yang–Mills theory

In this Letter, we consider lattice versions of the decomposition of the Yang–Mills field a la Cho–Faddeev–Niemi, which was extended by Kondo, Shinohara and Murakami in the continuum formulation. For the SU(N)$\mathit{SU}(N)$ gauge group, we propose a set of defining equations for specifying the decomposition of the gauge link variable and solve them exactly without using the ansatz adopted in the previous studies for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$. As a result, we obtain the general form of the decomposition for SU(N)$\mathit{SU}(N)$ gauge link variables and confirm the previous results obtained for SU(2)$\mathit{SU}(2)$ and SU(3)$\mathit{SU}(3)$.     

Type II seesaw mechanism for Higgs doublets and the scale of new physics

We elaborate on an earlier proposal by Ernest Ma of a type II seesaw mechanism for suppressing the vacuum expectation values of some Higgs doublets. We emphasize that, by nesting this form of seesaw mechanism into various other seesaw mechanisms, one may obtain light neutrino masses in such a way that the new-physics scale present in the seesaw mechanism—the masses of scalar gauge-SU(2)$\mathit{SU}(2)$ triplets, scalar SU(2)$\mathit{SU}(2)$ doublets, or right-handed neutrinos—does not need to be higher than a few 10 TeV. We also investigate other usages of the type II seesaw mechanism for Higgs doublets. For instance, the suppression of the vacuum expectation values of Higgs doublets may realize Froggatt–Nielsen suppression factors in some entries of the fermion mass matrices.     

On neutrino masses via CPT violating Higgs interaction in the Standard Model

The Lorentz invariant CPT   violation by using non-local interactions is naturally incorporated in the Higgs coupling to neutrinos in the Standard Model, without spoiling the basic SU_(2)L×U(1)$\mathit{SU}{(2)}_L\times U(1)$ gauge symmetry. The neutrino–antineutrino mass splitting is thus realized by the mechanism which was proposed recently, assuming the neutrino masses to be predominantly Dirac-type in the Standard Model.     

Supersymmetric grand unification with light color-triplet

We construct a natural model of the supersymmetric SU(6)$\mathit{SU}(6)$ unification, in which the symmetry breaking, down to the standard model gauge group, results in the number of pseudo-Nambu–Goldstone superfields with interesting properties. Namely, besides the Higgs doublet–antidoublet pair which is responsible for the electroweak phase transition, the Nambu–Goldstone sector consists of multiplets in the anti- and fundamental representations of SU(5)$\mathit{SU}(5)$. While being strictly massless in the supersymmetric limit, they acquire the weak scale masses as a result of its breaking. The color-triplet components of this light sector could, in principle, mediate an unacceptably fast proton decay; however, because of the natural TeV/_MGUT$\text{TeV}/M_{\mathrm{GUT}}$ suppression of the Yukawa couplings to the light quarks and leptons, their existence is compatible with the experimental bound on proton lifetime. This suppression is made further interesting, since it results in the lifetime, of the lightest of the above-mentioned colored particles from 1 s to 1 day$1\text{day}$, long enough for it to appear stable in the detector. Furthermore, we argue that the accommodation of the color-triplet pseudo-Nambu–Goldstones, without fine-tuning or contradicting observations, implies SU(6)$\mathit{SU}(6)$ unification.     

Unity of elementary particles and forces for the third family

We propose a non-supersymmetric SU(5)$\mathit{SU}(5)$ model in which only the third family of fermions are unified. The model remedies the non-unification of the three Standard Model couplings in non-supersymmetric SU(5)$\mathit{SU}(5)$. It also provides a mechanism for baryon number violation which is needed for the baryon asymmetry of the Universe and is not present in the Standard Model. Current experimental constraints on the leptoquark gauge bosons, mediating such baryon and lepton violating interactions in our model, allow their masses to be at the TeV scale. These can be searched for as a (bτ) or (tt) resonance at the Large Hadron Collider as predicted in our model.     

The 't Hooft–Polyakov monopole in the presence of a 't Hooft operator

We present explicit BPS field configurations representing one non-Abelian monopole with one minimal weight 't Hooft operator insertion. We explore the SO(3)$\mathit{SO}(3)$ and SU(2)$\mathit{SU}(2)$ gauge groups. In the case of SU(2)$\mathit{SU}(2)$ gauge group the minimal 't Hooft operator can be completely screened by the monopole. If the gauge group is SO(3)$\mathit{SO}(3)$, however, such screening is impossible. In the latter case we observe a different effect of the gauge symmetry enhancement in the vicinity of the 't Hooft operator.     

Modifications to the properties of the Higgs boson

We explore the impact of new SU(3)×SU(2)×U(1)$\mathit{SU}(3)\times \mathit{SU}(2)\times U(1)$ invariant interactions characterized by a scale of order a TeV on Higgs boson properties. The Higgs production rate and branching ratios can be very different from their standard model values. We also discuss the possibility that these new interactions contribute to acceptable unification of the gauge couplings.     

Six-dimensional Yang black holes in dilaton gravity

We study the six-dimensional dilaton gravity Yang black holes of Bergshoeff, Gibbons and Townsend, which carry (1,−1)$(1,-1)$ charge in SU(2)×SU(2)$\mathit{SU}(2)\times \mathit{SU}(2)$ gauge group. We find what values of the asymptotic parameters (mass and scalar charge) lead to a regular horizon, and show that there are no regular solutions with an extremal horizon.     

The Harari–Shupe preon model and nonrelativistic quantum phase space

We propose that the whole algebraic structure of the Harari–Shupe rishon model originates via a Dirac-like linearization of quadratic form x²+p²${\mathbf{x}}^2+{\mathbf{p}}^2$, with position and momentum satisfying standard commutation relations. The scheme does not invoke the concept of preons as spin-1/2 subparticles, thus evading the problem of preon confinement, while fully explaining all symmetries emboded in the Harari–Shupe model. Furthermore, the concept of quark colour is naturally linked to the ordering of rishons. Our scheme leads to group U(1)⊗SU(3)$U(1)\otimes \mathit{SU}(3)$ combined with SU(2)$\mathit{SU}(2)$, with two of the SU(2)$\mathit{SU}(2)$ generators not commuting with reflections. An interpretation of intra-generation quark–lepton transformations in terms of genuine rotations and reflections in phase space is proposed.     

Inverted neutrino mass hierarchy and new signals of a chromophobic charged Higgs at the Large Hadron Collider

We explore the signals of a charged Higgs arising in a two Higgs doublet model respecting SUL₍₂₎×U(1)×Z₂$\mathit{SU}{(2)}_L\times U(1)\times Z_2$ symmetry with three singlet right-handed neutrinos, NR$N_R$. The charged Higgs in this model has negligible coupling with quarks, and has unsuppressed coupling to leptons and neutrinos. This leads to novel signatures of the charged Higgs at the LHC, especially in the case of an inverted neutrino mass hierarchy, in the form of electrons and muons with missing energy.     

Zero modes for the boundary giant magnons

We study the fermion zero-mode dynamics for open strings ending on the giant graviton branes. For the open string ending on the Z=0$Z=0$ brane, the quantization of the fermion zero-modes of boundary giant magnons reproduces the 256 states of the boundary degrees with the precise realization of the SU(2|2)×SU(2|2)$\mathit{SU}(2|2)\times \mathit{SU}(2|2)$ symmetry algebra. Also for the open string ending on the Y=0$Y=0$ brane, we reproduce the unique vacuum state from the fermion zero-modes.     

Hyperboloid,instanton, oscillator

We suggest the exactly solvable model of the oscillator on a four-dimensional hyperboloid which interacts with a SU(2)$\mathit{SU}(2)$ instanton. We calculate its wavefunctions and spectrum.     

Two-component gadget for transforming any two nonorthogonal polarization states into one another

We present an algorithm for transforming an arbitrary input polarization state into a nonorthogonal but otherwise arbitrary output polarization state, by using two quarter-wave retarders. Such an array reduces the number of retarders employed in the well-known Simon–Mukunda gadget, which consists of one half-wave and two quarter-wave retarders. The latter was designed to realize arbitrary SU(2)$\mathit{SU}(2)$ transformations on qubits. The gadget presented here accomplishes a related task, allowing to transforming an input qubit into a target qubit, by choosing a particular SU(2)$\mathit{SU}(2)$ transformation that is realizable with two quarter-wave plates.     

What is the minimal supersymmetric Standard Model from F-theory?

We construct gauge theory of SU(3)×SU(2)×U(1)$\mathit{SU}(3)\times \mathit{SU}(2)\times U(1)$ by spectral cover from F-theory and ask how the Standard Model is extended under minimal assumptions on Higgs sector. For the requirement on different numbers between Higgs pairs and matter generations (respectively one and three) distinguished by R-parity, we choose a universal G  -flux obeying SO(10)$\mathit{SO}(10)$ but slightly breaking _E6$E_6$ unification relation. This condition forces distinction between up and down Higgs fields, suppression of proton decay operators up to dimension five, and existence and dynamics of a singlet related to μ-parameter.     

Two-dimensional gauge theory and matrix model

We study a matrix model obtained by dimensionally reducing Chern–Simons theory on S³$S^3$. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2)$\mathit{SU}(2)$. We show that the N  -block sectors reproduce SU(N)$\mathit{SU}(N)$ Yang–Mills theory on S²$S^2$ as the matrix size goes to infinity.     

Matrix regularization of embedded 4-manifolds

We consider products of two 2-manifolds such as S²×S²$S^2\times S^2$, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N)$\mathit{SU}(N)\otimes \mathit{SU}(N)$ i.e. functions on a manifold are approximated by the Kronecker product of two SU(N)$\mathit{SU}(N)$ matrices.     

Symbiotic symmetries of the two-Higgs-doublet model

The new phenomenon of symbiotic symmetries   is described in the context of the Two-Higgs-Doublet Model (THDM). The quartic potential has two or more separate sectors with unequal symmetries, but these unequal symmetries persist even though the different sectors are renormalized by one another. We discuss all such symmetries of the THDM, consistent with the SU(2)×U(1)$\mathit{SU}(2)\times U(1)$ gauge interactions, using the Pauli formalism.     

Towards a Loop Quantum Gravity and Yang–Mills unification

We propose a new method of unifying gravity and the Standard Model by introducing a spin-foam model. We realize a unification between an SU(2)$\mathit{SU}(2)$ Yang–Mills interaction and 3D   general relativity by considering a constrained Spin(4)∼SO(4)$\mathrm{Spin}(4)\sim \mathit{SO}(4)$ Plebanski action. The theory is quantized à la   spin-foam by implementing the analogue of the simplicial constraints for the Spin(4)$\mathrm{Spin}(4)$ symmetry, providing a way to couple Yang–Mills fields to spin-foams. A natural 4D extension of the theory is introduced. We also present a way to recover 2-point correlation functions between the connections as a first way to implement scattering amplitudes between particle states, aiming to connect Loop Quantum Gravity to new physical predictions.