We numerically investigate the gravitational collapse of collisionless particles in spheroidal configurations both in four- and five-dimensional (5D) space-time. We repeat the simulation performed by Shapiro and Teukolsky (1991) that announced an appearance of a naked singularity, and also find similar results in the 5D version. That is, in a collapse of a highly prolate spindle, the Kretschmann invariant blows up outside the matter and no apparent horizon forms. We also find that the collapses in 5D proceed more rapidly than in 4D, and the critical prolateness for the appearance of an apparent horizon in 5D is loosened, compared to 4D cases. We also show how collapses differ with spatial symmetries comparing 5D evolutions in single-axisymmetry, SO(3), and those in double-axisymmetry, $\mathrm{U}(1)\times \mathrm{U}(1)$.

The Galileon model was recently proposed to locally describe a class of modified gravity theories, including the braneworld Dvali-Gabadadze-Porrati model. We discuss spontaneous symmetry breaking of the self-accelerating branch in a multi-Galileon theory with internal global symmetries. We show that a modified version of Goldstone’s theorem is applicable to the symmetry breaking pattern and discuss its implications. We also derive the Hamiltonian of a general multi-Galileon theory and discuss its implications.

We investigate the hydrostatic equilibrium of stellar structure by taking into account the modified Lané-Emden equation coming out from $f(R)$ gravity. Such an equation is obtained in a metric approach by considering the Newtonian limit of $f(R)$ gravity, which gives rise to a modified Poisson equation, and then introducing a relation between pressure and density with polytropic index $n$. The modified equation results an integro-differential equation, which, in the limit $f(R)\to R$, becomes the standard Lané-Emden equation. We find the radial profiles of the gravitational potential by solving for some values of $n$. The comparison of solutions with those coming from general relativity shows that they are compatible and physically relevant.

The standard cold dark matter cosmological model, while successful in explaining the observed large scale structure of the Universe, tends to overpredict structure on small scales. It has been proposed this problem may be alleviated in a class of late-decaying dark matter models, in which the parent dark matter particle decays to an almost degenerate daughter, plus a relativistic final state. We construct explicit particle physics models that realize this goal while obeying observational constraints. To achieve this, we introduce a pair of fermionic dark matter candidates and a new scalar field, which obey either a ${\mathbb{Z}}_4$ or a $U(1)$ symmetry. Through the spontaneous breaking of these symmetries, and coupling of the new fields to standard model particles, we demonstrate that the desired decay process may be obtained. We also discuss the dark matter production processes in these models.

We present a statistic for the detection of stochastic gravitational wave backgrounds (SGWBs) using radiometry with a network of multiple baselines. We also quantitatively compare the sensitivities of existing baselines and their network to SGWBs. We assess how the measurement accuracy of signal parameters, e.g., the sky position of a localized source, can improve when using a network of baselines, as compared to any of the single participating baselines. The search statistic itself is derived from the likelihood ratio of the cross correlation of the data across all possible baselines in a detector network and is optimal in Gaussian noise. Specifically, it is the likelihood ratio maximized over the strength of the SGWB and is called the maximized-likelihood ratio (MLR). One of the main advantages of using the MLR over past search strategies for inferring the presence or absence of a signal is that the former does not require the deconvolution of the cross correlation statistic. Therefore, it does not suffer from errors inherent to the deconvolution procedure and is especially useful for detecting weak sources. In the limit of a single baseline, it reduces to the detection statistic studied by Ballmer [Classical Quantum Gravity 23, S179 (2006).] and Mitra et al. [Phys. Rev. D 77, 042002 (2008).]. Unlike past studies, here the MLR statistic enables us to compare quantitatively the performances of a variety of baselines searching for a SGWB signal in (simulated) data. Although we use simulated noise and SGWB signals for making these comparisons, our method can be straightforwardly applied on real data.

Corresponding to the similarity between the Lorentz gauge ${\partial }_{\mu }{A}^{\mu }=0$ in electrodynamics and $g^{\mu \nu }{\Gamma }_{\mu \nu }^{\rho }=0$ in gravity, we show that the counterpart of the radiation gauge ${\partial }_i{A}^i=0$ is $g^{ij}{\Gamma }_{ij}^{\rho }=0$, instead of other forms as discussed before. Particularly, 1) at least for a weak field, $g^{ij}{\Gamma }_{ij}^{\rho }=0$ fixes the gauge completely and picks out exactly the two physical components of the gravitational field; 2) like $A^0$, the nondynamical components $h_{0\mu }$ are solved instantaneously; 3) gravitational radiation is generated by the “transverse” part of the energy-momentum tensor, similar to the transverse current ${\overrightarrow{J}}_{\perp }$. This “true” radiation gauge $g^{ij}{\Gamma }_{ij}^{\rho }=0$ is especially pertinent for studying gravitational energy, such as the energy flow in gravitational radiation. It agrees with the transverse-traceless gauge for a pure wave, and reveals remarkably how the transverse-traceless gauge can be adapted in the presence of source.

We study the fermion mass and mixing hierarchy problems within the context of the $SU(5)$ $4+1\mathrm{d}$ domain-wall brane model of Davies, George, and Volkas. In this model, the ordinary fermion mass relations of $SU(5)$ grand unified theories are avoided, since the masses are proportional to overlap integrals of the profiles of the electroweak Higgs and the chiral components of each fermion, which are split into different $3+1\mathrm{d}$ hyperplanes according to their hypercharges. We show that the fermion mass hierarchy without electroweak mixing can be generated naturally from these splittings, that generation of the Cabibbo-Kobayashi-Maskawa matrix looks promising, and that the Cabibbo angle, along with the mass hierarchy, can be generated for the case of Majorana neutrinos from a more modest hierarchy of parameters. We also show that, under some assumptions made on the parameter space, the generation of realistic lepton mixing angles is not possible without fine-tuning, which argues for a flavor symmetry to enforce the required relations.

The dominant production process for heavy charged-Higgs bosons at the LHC is the associated production with heavy quarks. We have calculated the next-to-leading-order supersymmetric QCD corrections to charged-Higgs production through the parton processes $q\overline{q},\mathrm{gg}\to \mathrm{tb}{\mathrm{H}}^{\pm }$ and present results for total cross sections and differential distributions. The QCD corrections reduce the renormalization and factorization scale dependence and thus stabilize the theoretical predictions. We present a comparison of the next-to-leading-order results for the inclusive cross section with a calculation based on bottom-gluon fusion $\mathrm{gb}\to \mathrm{t}{\mathrm{H}}^{\pm }$ and discuss the impact of the next-to-leading-order corrections on charged-Higgs searches at the LHC.

The possibility of observing associated production of the charged Higgs and $W$ boson in the framework of the minimal supersymmetric standard model (MSSM) at LHC is studied. Both leptonic and hadronic decays of the $W$ boson are studied while the charged Higgs boson is considered to decay to a $\tau$ lepton and a neutrino. Therefore two search categories are defined based on the leptonic and hadronic final states, i.e., $\ell \tau +E_T^{\mathrm{miss}}$ and $jj\tau +E_T^{\mathrm{miss}}$ where $\ell =e$ or $\mu$ and $j$ is a light jet from $W$ decay. The discovery chance of the two categories is evaluated at an integrated luminosity of $300{\mathrm{fb}}^{-1}$ at LHC. It is shown that both leptonic and hadronic final states have the chance of discovery at high $\tan \beta$. Finally $5\sigma$ and $3\sigma$ contours are provided for both search categories.

We investigate in detail “instantaneous interquark potentials,” interesting gauge-dependent quantities defined from the spatial correlators of the temporal link-variable $U_4$, in generalized Landau gauge using SU(3) quenched lattice QCD. The instantaneous $\mathrm{Q}\overline{\mathrm{Q}}$ potential has no linear part in the Landau gauge, and it is expressed by the Coulomb plus linear potential in the Coulomb gauge, where the slope is 2–3 times larger than the physical string tension. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and its linear part rapidly grows in the neighborhood of the Coulomb gauge. We also investigate the instantaneous 3Q potential in the generalized Landau gauge, and obtain similar results to the $\mathrm{Q}\overline{\mathrm{Q}}$ case. $T$-length terminated Polyakov-line correlators and their corresponding “finite-time potentials” are also investigated in generalized Landau gauge.

We calculate the model-independent radiative corrections to the Dalitz plot of $K_{l3}^{\pm }$ decays to the order of $(\alpha /\pi )(q/M_1)$, where $q$ is the momentum transfer and $M_1$ is the mass of the kaon. The final results are presented, first, with the triple integration over the variables of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. These two forms are useful to cross-check on one another and with other calculations. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability.

We present new constraints on the neutrino oscillation parameters $\Delta m_{21}^2$, ${\theta }_{12}$, and ${\theta }_{13}$ from a three-flavor analysis of solar and KamLAND data. The KamLAND data set includes data acquired following a radiopurity upgrade and amounts to a total exposure of $3.49\times {10}^{32}$ target-proton-year. Under the assumption of $CPT$ invariance, a two-flavor analysis (${\theta }_{13}=0$) of the KamLAND and solar data yields the best-fit values ${tan}^2{\theta }_{12}={0.444}_{-0.030}^{+0.036}$ and $\Delta m_{21}^2={7.50}_{-0.20}^{+0.19}\times {10}^{-5}{\mathrm{eV}}^2$; a three-flavor analysis with ${\theta }_{13}$ as a free parameter yields the best-fit values ${tan}^2{\theta }_{12}={0.452}_{-0.033}^{+0.035}$, $\Delta m_{21}^2={7.50}_{-0.20}^{+0.19}\times {10}^{-5}{\mathrm{eV}}^2$, and ${sin}^2{\theta }_{13}={0.020}_{-0.016}^{+0.016}$. This ${\theta }_{13}$ interval is consistent with other recent work combining the CHOOZ, atmospheric and long-baseline accelerator experiments. We also present a new global ${\theta }_{13}$ analysis, incorporating the CHOOZ, atmospheric, and accelerator data, which indicates ${sin}^2{\theta }_{13}={0.009}_{-0.007}^{+0.013}$. A nonzero value is suggested, but only at the 79% C.L.

We examine lepton number violation (LNV) in theories with a saturated black hole bound on a large number of species. Such theories have been advocated recently as a possible solution to the hierarchy problem and an explanation of the smallness of neutrino masses. On the other hand, the violation of the lepton number can be a potential phenomenological problem of this $N$-copy extension of the standard model as due to the low quantum gravity scale black holes may induce TeV scale LNV operators generating unacceptably large rates of LNV processes. We show, however, that this issue can be avoided by introducing a spontaneously broken $U_{1(B-L)}$. Then, due to the existence of a specific compensation mechanism between contributions of different Majorana neutrino states, LNV processes in the standard model copy become extremely suppressed with rates far beyond experimental reach.

By using the gauge/gravity duality, we investigate the dual field theories of the anisotropic backgrounds, which are exact solutions of Einstein-Maxwell-dilaton theory with a Liouville potential. When we turn on the bulk gauge field fluctuation $A_x$ with a nontrivial dilaton coupling, the AC conductivity of this dual field theory is proportional to the frequency with an exponent depending on parameters of the anisotropic background. In some parameter regions, we find that this conductivity can have the negative exponent like the strange metal. In addition, we also investigate another $U(1)$ gauge field fluctuation, which is not coupled with a dilaton field. We classify all possible conductivities of this system and find that the exponent of the conductivity is always positive.

Hopf solitons in the Skyrme-Faddeev model are stringlike topological solitons classified by the integer-valued Hopf charge. In this paper we introduce an approximate description of Hopf solitons in terms of elastic rods. The general form of the elastic rod energy is derived from the field theory energy and is found to be an extension of the classical Kirchhoff rod energy. Using a minimal extension of the Kirchhoff energy, it is shown that a simple elastic rod model can reproduce many of the qualitative features of Hopf solitons in the Skyrme-Faddeev model. Features that are captured by the model include the buckling of the charge three solution, the formation of links at charges five and six, and the minimal energy trefoil knot at charge seven.

We investigate strong field vacuum effects using a phase-space approach based on the Wigner formalism. We calculate the Wigner function in a strong null-field background exactly, using lightfront field theory. The Wigner function exhibits the distinct features of strong field QED: in particular, we identify the effective mass in a laser pulse, compare it to the well-known mass shift in a periodic plane wave and identify signals of multiphoton absorption and emission. Finally, we show how to extend our results to describe vacuum pair production in colliding laser pulses.

Schwinger-Dyson equations are used to study spontaneous chiral and parity symmetry breaking of three-dimensional quantum electrodynamics with two-component fermions. This theory admits a topological photon mass that explicitly breaks parity symmetry and generates a fermion mass. We show for the first time that it is possible to spontaneously break both parity and chiral symmetry. We also find that chiral symmetry is restored at a critical number of fermion flavors in our truncation scheme. Finally, the Coleman-Hill theorem is used to demonstrate that the results are reasonably accurate.

We give the Lagrangian formulation of a generic nonminimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first-order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact $pp$-wave solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton.

As one of the most powerful probes of cosmological structure formation, the abundance of massive galaxy clusters is a sensitive probe of modifications to gravity on cosmological scales. In this paper, we present results from $N$-body simulations of a general class of $f(R)$ models, which self-consistently solve the nonlinear field equation for the enhanced forces. Within this class we vary the amplitude of the field, which controls the range of the enhanced gravitational forces, both at the present epoch and as a function of redshift. Most models in the literature can be mapped onto the parameter space of this class. Focusing on the abundance of massive dark matter halos, we compare the simulation results to a simple spherical collapse model. Current constraints lie in the large-field regime, where the chameleon mechanism is not important. In this regime, the spherical collapse model works equally well for a wide range of models and can serve as a model-independent tool for placing constraints on $f(R)$ gravity from cluster abundance. Using these results, we show how constraints from the observed local abundance of X-ray clusters on a specific $f(R)$ model can be mapped onto other members of this general class of models.

We calculate the critical temperature and free energy of the gluon plasma using the dilaton potential [B. Galow, E. Megias, J. Nian, and H. J. Pirner, Nucl. Phys. B834, 330 (2010).] in the gravity theory of anti-de Sitter/QCD. The finite temperature observables are calculated in two ways: first, from the Page-Hawking computation of the free energy, and secondly using the Bekenstein-Hawking proportionality of the entropy with the area of the horizon. Renormalization is well defined, because the $T=0$ theory has asymptotic freedom. We further investigate the change of the critical temperature with the number of flavors induced by the change of the running coupling constant in the quenched theory. The finite temperature behavior of the speed of sound, spatial string tension and vacuum expectation value of the Polyakov loop follow from the corresponding string theory in $Ad{S}_5$.