In recent work, we derived the long-distance confining dynamics of certain QCD-like gauge theories formulated on small $S^1\times {\mathbb{R}}^3$ based on symmetries, an index theorem, and Abelian duality. Here, we give the microscopic derivation. The solution reveals a new mechanism of confinement in QCD(adj) in the regime where we have control over both perturbative and nonperturbative aspects. In particular, consider $SU(2)$ QCD(adj) theory with $1\le n_f\le 4$ Majorana fermions, a theory which undergoes gauge symmetry breaking at small $S^1$. If the magnetic charge of the Bogomol’nyi-Prasad-Sommerfield (BPS) monopole is normalized to unity, we show that confinement occurs due to condensation of objects with magnetic charge 2, not 1. Because of index theorems, we know that such an object cannot be a two identical monopole configuration. Its net topological charge must vanish, and hence it must be topologically indistinguishable from the perturbative vacuum. We construct such non-self-dual topological excitations, the magnetically charged, topologically null molecules of a BPS monopole and $\overline{\mathrm{KK}}$ antimonopole, which we refer to as magnetic bions. An immediate puzzle with this proposal is the apparent Coulomb repulsion between the BPS-$\overline{\mathrm{KK}}$ pair. An attraction which overcomes the Coulomb repulsion between the two is induced by $2n_f$-fermion exchange. Bion condensation is also the mechanism of confinement in $\mathcal{N}=1$ SYM on the same four-manifold. The $SU(N)$ generalization hints a possible hidden integrability behind nonsupersymmetric QCD of affine Toda type, and allows us to analytically compute the mass gap in the gauge sector. We currently do not know the extension to ${\mathbb{R}}^4$.

In the nonrelativistic theory of gravitation recently proposed by Hořava, the Hamiltonian constraint is not a local equation satisfied at each spatial point but an equation integrated over a whole space. The global Hamiltonian constraint is less restrictive than its local version, and allows a richer set of solutions than in general relativity. We show that a component which behaves like pressureless dust emerges as an “integration constant” of dynamical equations and momentum constraint equations. Consequently, classical solutions to the infrared limit of Hořava-Lifshitz gravity can mimic general relativity plus cold dark matter.

It has long been known that null unstable geodesics are related to the characteristic modes of black holes—the so-called quasinormal resonances. The basic idea is to interpret the free oscillations of a black hole in the eikonal limit in terms of null particles trapped at the unstable circular orbit and slowly leaking out. The real part of the complex quasinormal resonances is related to the angular velocity at the unstable null geodesic. The imaginary part of the resonances is related to the instability time scale (or the inverse Lyapunov exponent) of the orbit. While this geometric-optics description of the black-hole quasinormal resonances in terms of perturbed null rays is very appealing and intuitive, it is still highly important to verify the validity of this approach by directly analyzing the Teukolsky wave equation which governs the dynamics of perturbation waves in the black-hole spacetime. This is the main goal of the present paper. We first use the geometric-optics technique of perturbing a bundle of unstable null rays to calculate the resonances of near-extremal Kerr black holes in the eikonal approximation. We then directly solve the Teukolsky wave equation (supplemented by the appropriate physical boundary conditions) and show that the resultant quasinormal spectrum obtained directly from the wave analysis is in accord with the spectrum obtained from the geometric-optics approximation of perturbed null rays.

CONTEXT: In this work we propose a modified gravity action $f(R)=(R^n-R_0^n{)}^{1/n}$ with two free parameters of $n$ and $R_0$ and derive the dynamics of a universe for this action in the Palatini formalism. AIM: We do a cosmological comparison of this model with observed data to find the best parameters of a model in a flat universe. METHOD: To constrain the free parameters of model we use SNIa type Ia data in two sets of gold and union samples, CMB-shift parameter, baryon acoustic oscillation, gas mass fraction in cluster of galaxies, and large-scale structure data. RESULT: The best fit from the observational data results in the parameters of model in the range of $n={0.98}_{-0.08}^{+0.08}$ and ${\Omega }_M={0.25}_{+0.1}^{-0.1}$ with one sigma level of confidence where a standard $\Lambda \mathrm{CDM}$ universe resides in this range of solution.

We refute recent claims in the literature that stars with relativistically deep potentials cannot exist in $f(R)$ gravity. Numerical examples of stable stars, including relativistic ($G{M}_{\star }/r_{\star }\sim 0.1$), constant density stars, are studied. As a star is made larger, nonlinear “chameleon” effects screen much of the star’s mass, stabilizing gravity at the stellar center. Furthermore, we show that the onset of this chameleon screening is unrelated to strong gravity. At large central pressures $P>\rho /3$, $f(R)$ gravity, like general relativity, does have a maximum gravitational potential, but at a slightly smaller value: $G{M}_{\star }/r_{\star }{|}_{\max }=0.345<4/9$ for constant density and one choice of parameters. This difference is associated with negative central curvature $R$ under general relativity not being accessed in the $f(R)$ model, but does not apply to any known astrophysical object.

We investigate the collapse of differentially rotating supermassive stars (SMSs) by means of $3+1$ hydrodynamic simulations in general relativity. We particularly focus on the onset of collapse to understand the final outcome of collapsing SMSs. We find that the estimated ratio of the mass between the black hole and the surrounding disk from the equilibrium star is roughly the same as the results from numerical simulation. This suggests that the picture of axisymmetric collapse is adequate, in the absence of nonaxisymmetric instabilities, to illustrate the final state of the collapse. We also find that quasiperiodic gravitational waves continue to be emitted after the quasinormal mode frequency has decayed. We furthermore have found that when the newly formed black hole is almost extreme Kerr, the amplitude of the quasiperiodic oscillation is enhanced during the late stages of the evolution. Geometrical features, shock waves, and instabilities of the fluid are suggested as a cause of this amplification behavior. This alternative scenario for the collapse of differentially rotating SMSs might be observable by the Laser Interferometer Space Antenna.

Recent astrophysical observations have motivated novel theoretical models of the dark matter sector. A class of such models predicts the existence of GeV scale cosmic strings that communicate with the standard model sector by Aharonov-Bohm interactions with electrically charged particles. We discuss the cosmology of these “dark strings” and investigate possible observational signatures. More elaborate dark sector models are argued to contain hybrid topological defects that may also have observational signatures.

A potential flux of high-energy neutrinos from the annihilation of dark matter particles trapped within the Sun has been exploited to place indirect limits on particle dark matter. In most models, the dark matter interacts weakly, but the possibility of a dark matter particle with a large cross section for elastic scattering on other dark matter particles has been proposed in several contexts. I study the consequences of such dark matter self-interactions for the high-energy neutrino flux from annihilation within the Sun. The self-interaction among dark matter particles may allow dark matter in the halo to be captured within the Sun by scattering off of dark matter particles that have already been captured within the Sun. This effect is not negligible in acceptable and accessible regions of parameter space. Enhancements in the predicted high-energy neutrino flux from the Sun of tens to hundreds of percent can be realized in broad regions of parameter space. Enhancements as large as factors of several hundred may be realized in extreme regions of the viable parameter space. Large enhancements require the dark matter annihilation cross section to be relatively small, $⟨{\sigma }_{\mathrm{A}}v⟩\lesssim {10}^{-27}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. This phenomenology is interesting. First, self-capture is negligible for the Earth, so dark matter self-interactions break the correspondence between the solar and terrestrial neutrino signals. Likewise, the correspondence between indirect and direct detection limits on scattering cross sections on nuclei is broken by the self-interaction. These broken correspondences may evince strong dark matter self-interactions. In some cases, self-capture can lead to observable indirect signals in regions of parameter space where limits from direct detection experiments would indicate that no such signal should be observable.

We suggest that the solution to the cosmological vacuum energy puzzle is linked to the infrared sector of the effective theory of gravity interacting with standard model fields. We propose a specific solvable two dimensional model where our proposal can be explicitly tested. We analyze the 2d Schwinger model on a 2-torus and in curved 2d space, mostly exploiting the properties of its topological susceptibility, its links with the nontrivial topology or deviations from spacetime flatness, and its relations to the real 4d world. The Kogut-Susskind ghost (which is a direct analogue of the Veneziano ghost in 4d) on a 2-torus and in curved 2d space plays a crucial role in the computation of the vacuum energy. The departure from Minkowski flatness, which is defined as the cosmological constant in our framework, is found to scale as $1/L$, where $L$ is the linear size of the torus. Therefore, in spite of the fact that the physical sector of 2d QED is represented by a single massive scalar particle, the deviation from Minkowski space is linear in $L$ rather than exponentially suppressed as one could naïvely expect.

Gluinos are produced pairwise at the LHC in quark-antiquark and gluon-gluon collisions: $q\overline{q}$, $gg\to \tilde{g}\tilde{g}$. While the individual polarization of gluinos vanishes in the limit in which the small mass difference between $L$ and $R$ squarks of the first two generations is neglected, nonzero spin-spin correlations are predicted within gluino pairs. If the squark/quark charges in Majorana gluino decays are tagged, the spin correlations have an impact on the energy and angular distributions in reconstructed final states. On the other hand, the gluino polarization in single gluino production in the supersymmetric Compton process $gq\to \tilde{g}{\tilde{q}}_{R,L}$ is predicted to be nonzero, and the polarization affects the final-state distributions in super-Compton events.

We postulate an exact permutation symmetry acting on ${10}^{32}$ standard model copies as the largest possible symmetry extension of the standard model. This setup automatically lowers the fundamental gravity cutoff down to TeV, and thus, accounts for the quantum stability of the weak scale. We study the phenomenology of this framework and show that below TeV energies the copies are well hidden, obeying all the existing observational bounds. Nevertheless, we identify a potential low energy window into the hidden world, the oscillation of the neutron into its dark copies. At the same time, proton decay can be suppressed by gauging the diagonal baryon number of the different copies. This framework offers an alternative approach to several particle physics questions. For example, we suggest a novel mechanism for generating naturally small neutrino masses that are suppressed by the number of neutrino species. The mirror copies of the standard model naturally house dark matter candidates. The general experimentally observable prediction of this scenario is an emergence of strong gravitational effects at the LHC. The low energy permutation symmetry powerfully constrains the form of this new gravitational physics and allows to make observational predictions, such as, production of micro black holes with very peculiar properties.

We calculate Compton scattering off an elementary spin $\frac{3}{2}$ particle in a recently proposed framework for the description of high spin fields based on the projection onto eigensubspaces of the Casimir operators of the Poincaré group. We also calculate this process in the conventional Rarita-Schwinger formalism. Both formalisms yield the correct Thomson limit but the predictions for the angular distribution and total cross section differ beyond this point. We point out that the average squared amplitudes in the forward direction for Compton scattering off targets with spin $s=0$, $\frac{1}{2}$, 1 are energy independent and have the common value $4e^4$. As a consequence, in the rest frame of the particle the differential cross section for Compton scattering in the forward direction is energy independent and coincides with the classical squared radius. We show that these properties are also satisfied by a spin $\frac{3}{2}$ target in the Poincaré projector formalism but not by the Rarita-Schwinger spin $\frac{3}{2}$ particle.

We study the 5D Rarita-Schwinger fields to describe spin $3/2$ baryons in AdS/QCD. We calculate the spectrum of spin $3/2$ baryons ($\Delta$ resonances) and their form factors, together with meson-baryon couplings from AdS/QCD. The transition form factors between $\Delta$ and nucleon are evaluated. Both pion and rho meson couplings have the same origin in the bulk and hence are unified. The numerical values for the meson-baryon transition couplings are roughly consistent with the values obtained from other methods. We also predict the numerical values of some new couplings associated with $\Delta$ resonances.

Reference [1] proposed a flavor model based on the symmetry group $S_4$, managing to describe fermion masses and mixings. The Weinberg operator has been used in order to provide the smallness of the neutrino masses, while a set of scalar fields, getting nonvanishing vacuum expectation values, spontaneously breaks down $S_4$ and provides the tri-bimaximal pattern as the lepton mixing matrix. Restricting to this setting, in this paper we analyze possible origins for the effective terms: the type I seesaw mechanism is the best known approach, but type II and III are also discussed. The phenomenology related to these models is various and future experiments could in principle discriminate among these proposals. Furthermore, we compare our realizations to two relevant $A_4$ based models, also predicting the tri-bimaximal lepton mixing, and we find that an analysis of the $0\nu 2\beta$-decay parameters could distinguish among all these realizations. The introduction of new physics beyond the standard model, like heavy right-handed neutrinos, scalar triplets, and fermion triplets, let us investigate leptogenesis, and this provides constraints in the realization of the models.

We discuss the three neutrino flavor evolution problem with general, flavor-diagonal, matter potentials and a fully parametrized mixing matrix that includes $CP$ violation, and derive expressions for the eigenvalues, mixing angles, and phases. We demonstrate that, in the limit that the mu and tau potentials are equal, the eigenvalues and matter mixing angles ${\tilde{\theta }}_{12}$ and ${\tilde{\theta }}_{13}$ are independent of the $CP$ phase, although ${\tilde{\theta }}_{23}$ does have $CP$ dependence. Since we are interested in developing a framework that can be used for $S$ matrix calculations of neutrino flavor transformation, it is useful to work in a basis that contains only off-diagonal entries in the Hamiltonian. We derive the “nonadiabaticity” parameters that appear in the Hamiltonian in this basis. We then introduce the neutrino $S$ matrix, derive its evolution equation and the integral solution. We find that this new Hamiltonian, and therefore the $S$ matrix, in the limit that the $\mu$ and $\tau$ neutrino potentials are the same, is independent of both ${\tilde{\theta }}_{23}$ and the $CP$ violating phase. In this limit, any $CP$ violation in the flavor basis can only be introduced via the rotation matrices, and so effects which derive from the $CP$ phase are then straightforward to determine. We then show explicitly that the electron neutrino and electron antineutrino survival probability is independent of the $CP$ phase in this limit. Conversely, if the $CP$ phase is nonzero and mu and tau matter potentials are not equal, then the electron neutrino survival probability cannot be independent of the $CP$ phase.

We discuss the impact of near detectors at a neutrino factory both on standard oscillation and nonstandard interaction measurements. Our systematics treatment includes cross section errors, flux errors, and background uncertainties, and our near detector fluxes include the geometry of the neutrino source and the detector. Instead of a specific detector concept, we introduce qualitatively different classes of near detectors with different characteristics, such as near detectors catching the whole neutrino flux (near detector limit) versus near detectors observing a spectrum similar to that of the far detector (far detector limit). We include the low energy neutrino factory in the discussion. We illustrate for which measurements near detectors are required, discuss how many are needed, and what the role of the flux monitoring is. For instance, we demonstrate that near detectors are mandatory for the leading atmospheric parameter measurements if the neutrino factory has only one baseline, whereas systematical errors partially cancel if the neutrino factory complex includes the magic baseline. Finally, near detectors with ${\nu }_{\tau }$ detection are shown to be useful for nonstandard interactions.

We present a search for decays of $B$ mesons to final states with a $b_1$ meson and a $\rho$ or $K^{*}(892)$ meson. The search is based on a data sample consisting of 465 million $B\overline{B}$ pairs collected by the BABAR detector at the SLAC National Accelerator Laboratory. We do not observe any statistically significant signal. The upper limits we set on the branching fractions range from 1.4 to $8.0\times {10}^{-6}$ at the 90% confidence level, including systematic uncertainties.

We investigate recovery of the bulk $S$ matrix from the AdS/CFT correspondence, at large radius. It was recently argued that some of the elements of the $S$ matrix might be read from CFT correlators, given a particular singularity structure of the latter, but leaving the question of more general $S$ matrix elements. Since in AdS/CFT, data must be specified on the boundary, we find certain limitations on the corresponding bulk wave packets and on their localization properties. In particular, those we have found that approximately localize have low-energy tails, and corresponding power-law tails in position space. When their scattering is compared to that of “sharper” wave packets typically used in scattering theory, one finds apparently significant differences, suggesting a possible lack of resolution via these wave packets. We also give arguments that construction of the sharper wave packets may require nonperturbative control of the boundary theory, and particularly of the $N^2$ matrix degrees of freedom. These observations thus raise interesting questions about what principle would guarantee the appropriate control, and about how a boundary CFT can accurately approximate the flat space $S$ matrix.

The aim of this paper is to investigate the separability of a spin-$1/2$ spinor field in a five-dimensional rotating, charged black hole constructed by Cvetič and Youm in string theory, in the case when three $U(1)$ charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-$1/2$ spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Stäckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.

We develop some ideas discussed by E. Schucking [arXiv:0803.4128] concerning the geometry of the gravitational field. First, we address the concept according to which the gravitational acceleration is a manifestation of the space-time torsion, not of the curvature tensor. It is possible to show that there are situations in which the geodesic acceleration of a particle may acquire arbitrary values, whereas the curvature tensor approaches zero. We conclude that the space-time curvature does not affect the geodesic acceleration. Then we consider the Pound-Rebka experiment, which relates the time interval $\Delta {\tau }_1$ of two light signals emitted at a position $r_1$, to the time interval $\Delta {\tau }_2$ of the signals received at a position $r_2$, in a Schwarzschild type gravitational field. The experiment is determined by four space-time events. The infinitesimal vectors formed by these events do not form a parallelogram in the $(t,r)$ plane. The failure in the closure of the parallelogram implies that the space-time has torsion. We find the explicit form of the torsion tensor that explains the nonclosure of the parallelogram.