Two loop finiteness of Higgs mass and potential in the gauge-Higgs unification

The zero mode of an extra-dimensional component of gauge potentials serves as a 4D Higgs field in the gauge-Higgs unification. We examine QED on $M^4 \times S^1$ and determine the mass and potential of a 4D Higgs field (the $A_5$ component) at the two loop level with gauge invariant reguralization. It is seen that the mass is free from divergences and independent of the renormalization scheme.Comment: 18 pages, 1 figur

Multi-Higgs Mass Spectrum in Gauge-Higgs Unification

We study an SU(2) supersymmetric gauge model in a framework of gauge-Higgs unification. Multi-Higgs spectrum appears in the model at low energy. We develop a useful perturbative approximation scheme for evaluating effective potential to study the multi-Higgs mass spectrum. We find that both tree-massless and massive Higgs scalars obtain mass corrections of similar size from finite parts of the loop effects. The corrections modify multi-Higgs mass spectrum, and hence, the loop effects are significant in view of future verifications of the gauge-Higgs unification scenario in high-energy experiments.Comment: 32 pages; typos corrected and a few comments added, published versio

Implication of Omega_m through the Morphological Analysis of Weak Lensing Fields

We apply the morphological descriptions of two-dimensional contour map, the so-called Minkowski functionals (the area fraction, circumference, and Euler characteristics), to the convergence field $\kappa(\bm{\theta})$ of the large-scale structure reconstructed from the shear map produced by the ray-tracing simulations. The perturbation theory of structure formation has suggested that the non-Gaussian features on the Minkowski functionals with respect to the threshold in the weakly nonlinear regime are induced by the three skewness parameters of $\kappa$ that are sensitive to the density parameter of matter, $\Omega_{\rm m}$. We show that, in the absence of noise due to the intrinsic ellipticities of source galaxies with which the perturbation theory results can be recovered, the accuracy of $\Omega_{\rm m}$ determination is improved by $\sim 20$ using the Minkowski functionals compared to the conventional method of using the direct measure of skewness.Comment: 4 pages, 3 figures, to appear in ApJ Lette

Model building by coset space dimensional reduction in ten-dimensions with direct product gauge symmetry

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and gauge group is a direct product of two Lie groups. We list up candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space,we find fermion and scalar representations of $G_{\mathrm{GUT}} \times U(1)$ with $G_{\mathrm{GUT}}=SU(5), SO(10)$ and $E_6$ which accomodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with a different dimension for $G_{\mathrm{GUT}}=SO(10)$ and $E_6$ models.Comment: 14 pages; added local report number, added refferenc

Non-Gaussianity Consistency Relation for Multi-field Inflation

While detection of the "local form" bispectrum of primordial perturbations would rule out all single-field inflation models, multi-field models would still be allowed. We show that multi-field models described by the $\delta N$ formalism obey an inequality between $f_{\rm NL}$ and one of the local-form {\it trispectrum} amplitudes, $\tau_{\rm NL}$, such that $\tau_{\rm NL}>\frac12(\frac65f_{\rm NL})^2$ with a possible logarithmic scale dependence, provided that 2-loop terms are small. Detection of a violation of this inequality would rule out most of multi-field models, challenging inflation as a mechanism for generating the primoridal perturbations.Comment: 5 pages. Accepted for publication in Physical Review Letter

Dynamical symmetry breaking in Gauge-Higgs unification of 5D N=1{\mathcal N}=1 SUSY theory

We study the dynamical symmetry breaking in the gauge-Higgs unification of the 5D ${\mathcal N}=1$ SUSY theory, compactified on an orbifold, $S^1/Z_2$. This theory identifies Wilson line degrees of freedoms as ``Higgs doublets''. We consider $SU(3)_c \times SU(3)_W$ and SU(6) models, in which the gauge symmetries are reduced to $SU(3)_c \times SU(2)_L \times U(1)_Y$ and $SU(3)_c \times SU(2)_L \times U(1)_Y \times U(1)$, respectively, through the orbifolding boundary conditions. Quarks and leptons are bulk fields, so that Yukawa interactions can be derived from the 5D gauge interactions. We estimate the one loop effective potential of ``Higgs doublets'', and analyze the vacuum structures in these two models. We find that the effects of bulk quarks and leptons destabilize the suitable electro-weak vacuum. We show that the introduction of suitable numbers of extra bulk fields possessing the suitable representations can realize the appropriate electro-weak symmetry breaking.Comment: 15 pages, 4 figures;disscutions on Higgs quartic couplings adde

R-mode Instability of Slowly Rotating Non-isentropic Relativistic Stars

We investigate properties of $r$-mode instability in slowly rotating relativistic polytropes. Inside the star slow rotation and low frequency formalism that was mainly developed by Kojima is employed to study axial oscillations restored by Coriolis force. At the stellar surface, in order to take account of gravitational radiation reaction effect, we use a near-zone boundary condition instead of the usually imposed boundary condition for asymptotically flat spacetime. Due to the boundary condition, complex frequencies whose imaginary part represents secular instability are obtained for discrete $r$-mode oscillations in some polytropic models. It is found that such discrete $r$-mode solutions can be obtained only for some restricted polytropic models. Basic properties of the solutions are similar to those obtained by imposing the boundary condition for asymptotically flat spacetime. Our results suggest that existence of a continuous part of spectrum cannot be avoided even when its frequency becomes complex due to the emission of gravitational radiation.Comment: 10 pages, 4 figures, accepted for publlication in PR

A general formula of the effective potential in 5D SU(N) gauge theory on orbifold

We show a general formula of the one loop effective potential of the 5D SU(N) gauge theory compactified on an orbifold, $S^1/Z_2$. The formula shows the case when there are fundamental, (anti-)symmetric tensor and adjoint representational bulk fields. Our calculation method is also applicable when there are bulk fields belonging to higher dimensional representations. The supersymmetric version of the effective potential with Scherk-Schwarz breaking can be obtained straightforwardly. We also show some examples of effective potentials in SU(3), SU(5) and SU(6) models with various boundary conditions, which are reproduced by our general formula.Comment: 22 pages;minor corrections;references added;typos correcte

Gauge Coupling Unification in GUT with Anomalous U(1) Symmetry

We show that in the framework of grand unified theory (GUT) with anomalous $U(1)_A$ gauge symmetry, the success of the gauge coupling unification in the minimal SU(5) GUT is naturally explained, even if the mass spectrum of superheavy fields does not respect SU(5) symmetry. Because the unification scale for most realizations of the theory becomes smaller than the usual GUT scale, it suggests that the present level of experiments is close to that sufficient to observe proton decay via dimension 6 operators, $p\to e+\pi$.Comment: 4 pages, RevTeX, to appear in Phys.Rev.Let

Numerical evolution of multiple black holes with accurate initial data

We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic solver. Using these initial data, we show the results for three black hole evolutions with sixth-order waveform convergence. We compare results obtained with the BAM and AMSS-NCKU codes with previous results. The approximate analytic solution to the Hamiltonian constraint used in previous simulations of three black holes leads to different dynamics and waveforms. We present some numerical experiments showing the evolution of four black holes and the resulting gravitational waveform.Comment: Published in PR