We present a detailed study on triminimal parametrizations of quark and lepton mixing matrices with different basis matrices. We start with a general discussion on the triminimal expansion of the mixing matrix and on possible unified quark and lepton parametrization using quark-lepton complementarity. We then consider several interesting basis matrices and compare the triminimal parametrizations with the Wolfenstein-like parametrizations. The usual Wolfenstein parametrization for quark mixing is a triminimal expansion around the unit matrix as the basis. The corresponding quark-lepton complementarity lepton mixing matrix is a triminimal expansion around the bimaximal basis. Current neutrino oscillation data show that the lepton mixing matrix is very well represented by the tribimaximal mixing. It is natural to take it as an expanding basis. The corresponding zeroth order basis for quark mixing in this case makes the triminimal expansion converge much faster than the usual Wolfenstein parametrization. The triminimal expansion based on tribimaximal mixing can be converted to the Wolfenstein-like parametrizations discussed in the literature. We thus have a unified description between different kinds of parametrizations for quark and lepton sectors: the standard parametrizations, the Wolfenstein-like parametrizations, and the triminimal parametrizations.

We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in $\mathcal{N}=4$ projective superspace based on them. These can be viewed as Chern-Simons theories with special matter content and couplings. We explore the relations of these actions with the $\mathcal{N}=2$ actions based on generalized 3-Lie algebras found earlier and relate them to the original Bagger-Lambert-Gustavsson action.

We derive from a general formulation of pure spinor string theory on type IIA backgrounds the specific form of the action for the ${\mathrm{AdS}}_4\times \mathbb{C}{P}^3$ background. We provide a complete geometrical characterization of the structure of the superfields involved in the action.

The Barbero-Immirzi (BI) parameter is promoted to a field and a canonical analysis is performed when it is coupled with a Nieh-Yan topological invariant. It is shown that, in the effective theory, the BI field is a canonical pseudoscalar minimally coupled with gravity. This framework is argued to be more natural than the one of the usual Holst action. Potential consequences in relation with inflation and the quantum theory are briefly discussed.

We consider the recently introduced “Galileon” field in a dynamical spacetime. When the Galileon is assumed to be minimally coupled to the metric, we underline that both field equations of the Galileon and the metric involve up to third-order derivatives. We show that a unique nonminimal coupling of the Galileon to curvature eliminates all higher derivatives in all field equations, hence yielding second-order equations, without any extra propagating degree of freedom. The resulting theory breaks the generalized “Galilean” invariance of the original model.

In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaître-Tolman-Bondi (timelike dust) spacetime containing a naked singularity. We decompose the angular part of the perturbation in terms of spherical harmonics and perform a Mellin transform to reduce the perturbation equations to a set of ordinary differential equations with singular points. We fix initial data so the perturbation is finite on the axis and the past null cone of the singularity, and follow the perturbation modes up to the Cauchy horizon. There we argue that certain scalars formed from the modes of the perturbation remain finite, indicating linear stability of the Cauchy horizon.

We consider a class of inflationary models with small oscillations imprinted on an otherwise smooth inflaton potential. These oscillations are manifest as oscillations in the power spectrum of primordial perturbations, which then give rise to oscillating departures from the standard cosmic microwave background power spectrum. We show that current data from the Wilkinson Microwave Anisotropy Probe constrain the amplitude of a sinusoidal variation in the inflaton potential to have an amplitude less than $3\times {10}^{-5}$. We anticipate that the smallest detectable such oscillations in Planck will be roughly an order of magnitude smaller, with slight improvements possible with a post-Planck cosmic-variance limited experiment.

Large-scale magnetic fields are observed today to be coherent on galactic scales. While there exists an explanation for their amplification and their specific configuration in spiral galaxies—the dynamo mechanism—a satisfying explanation for the original seed fields required is still lacking. Cosmic strings are compelling candidates because of their scaling properties, which would guarantee the coherence on cosmological scales of any resultant magnetic fields at the time of galaxy formation. We present a mechanism for the production of primordial seed magnetic fields from heterotic cosmic strings arising from $M$ theory. More specifically, we make use of heterotic cosmic strings stemming from $M5$-branes wrapped around four of the compact internal dimensions. These objects are stable on cosmological time scales and carry charged zero modes. Therefore a scaling solution of such defects will generate seed magnetic fields which are coherent on galactic scales today.

We investigate theoretically the interaction between charged particles and a plasma by calculating the scattering anisotropy. In several physical environments such as supernova shells, we expect strong stochastic magnetic fields. As shown, particle scattering is anisotropic in real physical situations even if the stochastic magnetic fields are isotropic and much stronger than the mean magnetic field. This anisotropic scattering result is very important for understanding diffusive shock acceleration, a mechanism which is usually thought to be responsible for the high energies of cosmic rays.

We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter $\mu$ ($\mu \ne 0$). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower falloff than the one relevant for general relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found that, at the chiral point $|\mu l|=1$ (where $l$ is the anti-de Sitter radius), allowing for logarithmic terms (absent for general relativity) in the asymptotic behavior of the metric makes both sets of Virasoro generators nonzero even though one of the central charges vanishes.

A fully relativistic analysis of gravitational lensing in tensor-vector-scalar (TeVeS) theory is presented. By estimating the lensing masses for a set of six lenses from the CASTLES database, and then comparing them to the stellar mass, the deficit between the two is obtained and analyzed. Considering a parametrized range for the TeVeS function $\mu (y)$, which controls the strength of the modification to gravity, it is found that on galactic scales TeVeS requires additional dark matter with the commonly used $\mu (y)$. A soft dependence of the results on the cosmological framework and the TeVeS free parameters is discussed. For one particular form of $\mu (y)$, TeVeS is found to require very little dark matter. This choice is however ruled out by rotation curve data. The inability to simultaneously fit lensing and rotation curves for a single form of $\mu (y)$ is a challenge to a no dark matter TeVeS proposal.

Unparticles are realized by deconstruction in higher extra dimensions. It is shown that in this framework when the scale invariance is broken, the corresponding spectral function of the unparticle is shifted by an amount of the breaking scale. The result strongly supports the conventional ansatz for the spectral function of the unparticle in the literature.

We study the role of fermionic resonances in realistic composite Higgs models. We consider the low energy effective description of a model in which the Higgs arises as the pseudo-Goldstone boson of an $SO(5)/SO(4)$ global symmetry breaking pattern. Assuming that only fermionic resonances are present below the cutoff of our effective theory, we perform a detailed analysis of the electroweak constraints on such a model. This includes the exact one-loop calculation of the $T$ parameter and the anomalous $Z{b}_L{\overline{b}}_L$ coupling for arbitrary new fermions and couplings. Other relevant observables like $b\to s\gamma$ and $\Delta B=2$ processes have also been examined. We find that, while minimal models are difficult to make compatible with electroweak precision tests, models with several fermionic resonances, such as the ones that appear in the spectrum of viable composite Higgs models from warped extra dimensions, are fully realistic in a large region of parameter space. These fermionic resonances could be the first observable signature of the model at the CERN LHC.

We propose a theoretical framework for $R$-parity violation. It is realized by a class of Calabi-Yau compactification of heterotic string theory. Trilinear $R$-parity violation in superpotential is either absent or negligibly small without an unbroken symmetry, due to a selection rule based on charge counting of a spontaneously broken U(1) symmetry. Although such a selection rule cannot be applied in general to nonrenormalizable operators in the low-energy effective superpotential, it is valid for terms trilinear in low-energy degrees of freedom, and hence can be used as a solution to the dimension-4 proton decay problem in the minimal supersymmetric standard model. Bilinear $R$-parity violation is generated, but there are good reasons why it is small enough to satisfy its upper bounds from neutrino mass and washout of baryon/lepton asymmetry. All $R$-parity violating dimension-5 operators can be generated. In this theoretical framework, nucleons can decay through squark-exchange diagrams combining dimension-5 and bilinear $R$-parity violating operators. $B-L$ breaking neutron decay is predicted.

Studying various thermodynamic quantities for the free domain wall fermions for both finite and infinite fifth dimensional extent $N_5$, we find that the lattice corrections are minimal for $N_T\ge 10$ for both energy density and susceptibility, for its irrelevant parameter $M$ in the range 1.45–1.50. The correction terms are, however, quite large for small lattice sizes of $N_T\le 8$. We propose modifications of the domain wall operator, as well as the overlap operator, to reduce the finite cutoff effects to within 10% of the continuum results of the thermodynamic quantities for the currently used $N_T=6–8$ lattices. Incorporating the chemical potential, we show that divergences proportional to ${\mu }^2/a^2$ are absent for a large class of such domain wall fermion actions although the chiral symmetry is broken for $\mu \ne 0$ at any finite lattice spacing.

The $SU(2)$-Higgs model, with a single Higgs field in the fundamental representation and a quartic self-interaction, has a Higgs region and a confinement region which are analytically connected in the parameter space of the theory; these regions thus represent a single phase. The effect of multiple Higgs fields on this phase structure is examined via Monte Carlo lattice simulations. For the case of $N\ge 2$ identical Higgs fields, there is no remaining analytic connection between the Higgs and confinement regions, at least when Lagrangian terms that directly couple different Higgs flavors are omitted. An explanation of this result in terms of enhancement from overlapping phase transitions is explored for $N=2$ by introducing an asymmetry in the hopping parameters of the Higgs fields. It is found that an enhancement of the phase transitions can still occur for a moderate (10%) asymmetry in the resulting hopping parameters.

We present cosmological solutions from the dimensionally reduced Chern-Simons term and obtain the smooth transition solution from the decelerated phase (AdS) to the accelerated phase (dS).

We investigate density perturbations generated through modulated reheating while inflation is driven by a conformally coupled scalar field. A large running of the spectral index is obtained, which reflects the basic nature of conformal inflation that higher-order time derivatives of the Hubble parameter during inflation are not necessarily small. This feature may allow us to distinguish between conformal inflation models and standard minimally coupled ones. We also investigate how the resulting fluctuations are modified when there is a deviation from an exact conformal coupling between the inflaton and gravity. Finally, we apply our results to the warped brane inflation model and see that observational bounds from the WMAP5 data suggest a blue tilted density perturbation spectrum.

We investigate the possibility of observing very small amplitude low frequency solar oscillations with the proposed laser interferometer space antenna (LISA). For frequencies $\nu$ below $3\times {10}^{-4}\mathrm{Hz}$ the dominant contribution is from the near zone time-dependent gravitational quadrupole moments associated with the normal modes of oscillation. For frequencies $\nu$ above $3\times {10}^{-4}\mathrm{Hz}$ the dominant contribution is from gravitational radiation generated by the quadrupole oscillations which is larger than the Newtonian signal by a factor of the order $(2\pi r\nu /c{)}^4$, where $r$ is the distance to the Sun, and $c$ is the velocity of light. The low order solar quadrupole pressure and gravity oscillation modes have not yet been detected above the solar background by helioseismic velocity and intensity measurements. We show that for frequencies $\nu \lesssim 2\times {10}^{-4}\mathrm{Hz}$, the signal due to solar oscillations will have a higher signal to noise ratio in a LISA type space interferometer than in helioseismology measurements. Our estimates of the amplitudes needed to give a detectable signal on a LISA type space laser interferometer imply surface velocity amplitudes on the sun of the order of $1–10\mathrm{mm}/\sec$ in the frequency range $1\times {10}^{-4}–5\times {10}^{-4}\mathrm{Hz}$. If such modes exist with frequencies and amplitudes in this range they could be detected with a LISA type laser interferometer.

We study higher derivative corrections to the statistical entropy function and the statistical entropy for five-dimensional Breckenridge-Myers-Peet-Vafa black holes by doing the asymptotic expansion of the partition function. This enables us to evaluate entropy for a large range of charges, even out of the Cardy (Farey tail) limit.