We investigate, via Monte Carlo simulations, the phase structure of a system of closed, nonintersecting but otherwise noninteracting, loops in 3 Euclidean dimensions. The loops correspond to closed trajectories of massive particles and we find a phase transition as a function of their mass. We identify the order parameter as the average length of the loops at equilibrium. This order parameter exhibits a sharp increase as the mass is decreased through a critical value, the behavior seems to be a crossover transition. We believe that the model represents an effective description of the broken-symmetry sector of the $2+1$ dimensional Abelian Higgs model, in the extreme strong coupling limit. The massive gauge bosons and the neutral scalars are decoupled, and the relevant low-lying excitations correspond to vortices and antivortices. The functional integral can be approximated by a sum over simple, closed vortex loop configurations. We present a novel fashion to generate nonintersecting closed loops, starting from a tetrahedral tessellation of three space. The two phases that we find admit the following interpretation: the usual Higgs phase and a novel phase which is heralded by the appearance of effectively infinitely long loops. We compute the expectation value of the Wilson loop operator and that of the Polyakov loop operator. The Wilson loop exhibits perimeter law behavior in both phases implying that the transition corresponds neither to the restoration of symmetry nor to confinement. The effective interaction between external charges is screened in both phases, however there is a dramatic increase in the polarization cloud in the novel phase as shown by the energy shift introduced by the Wilson loop.

The annihilation of dark matter particles captured by the Sun can lead to a neutrino flux observable in neutrino detectors. Considering the fact that these dark matter particles are nonrelativistic, if a pair of dark matter annihilates to a neutrino pair, the spectrum of neutrinos will be monochromatic. We show that in this case, even after averaging over the production point inside the Sun, the oscillatory terms of the oscillation probability do not average to zero. This leads to interesting observable features in the annual variation of the number of muon track events. We show that smearing of the spectrum due to thermal distribution of dark matter inside the Sun is too small to wash out this variation. We point out the possibility of studying the initial flavor composition of neutrinos produced by the annihilation of dark matter particles via measuring the annual variation of the number of $\mu$-track events in neutrino telescopes.

We consider the version of QCD in Euclidean Landau gauge in which the restriction to the Gribov region is implemented by a local, renormalizable action. This action depends on the Gribov parameter $\gamma$, with dimensions of $(\mathrm{\text{mass}}{)}^4$, whose value is fixed in terms of ${\Lambda }_{\mathrm{QCD}}$, by the gap equation, known as the horizon condition, $\frac{\partial \Gamma }{\partial \gamma }=0$, where $\Gamma$ is the quantum effective action. The restriction to the Gribov region suppresses gluons in the infrared, which nicely explains why gluons are not in the physical spectrum, but this only makes more mysterious the origin of the long-range force between quarks. In the present article we exhibit the symmetries of $\Gamma$, and show that the solution to the gap equation, which defines the classical vacuum, spontaneously breaks some of the symmetries of $\Gamma$. This implies the existence of massless Goldstone bosons and fermions that do not appear in the physical spectrum. Some of the Goldstone bosons may be exchanged between quarks, and are candidates for a long-range confining force. As an exact result we also find that in the infrared limit the gluon propagator vanishes like $k^2$.

The expectation value of Wilson loop operators in three-dimensional $\mathrm{SO}(N)$ Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polynomial arises as special cases: Sp(2), $\mathrm{SO}(-2)$, and $\mathrm{SL}(2,\mathbb{R})$. These results are confirmed and extended up to the second order, by means of perturbation theory, which moreover let us establish a duality relation between $\mathrm{SO}(\pm N)$ and $\mathrm{Sp}(\mp N)$ invariants. A correspondence between the first orders in perturbation theory of $\mathrm{SO}(-2)$, Sp(2) or SU(2) Chern-Simons quantum holonomy’s traces and the partition function of the $Q=4$ Potts model is built.

Nongravitating (stealth) scalar fields associated with Minkowski space in scalar-tensor gravity are examined. Analytical solutions for both nonminimally coupled scalar field theory and for Brans-Dicke gravity are studied and their stability with respect to tensor perturbations is assessed using a covariant and gauge-invariant formalism developed for alternative gravity. For Brans-Dicke solutions, the stability with respect to homogeneous perturbations is also studied. There are regions of parameter space corresponding to stability and other regions corresponding to instability.

String theory suggests the simultaneous presence of many ultralight axions, possibly populating each decade of mass down to the Hubble scale ${10}^{-33}\mathrm{eV}$. Conversely the presence of such a plenitude of axions (an axiverse) would be evidence for string theory, since it arises due to the topological complexity of the extra-dimensional manifold and is ad hoc in a theory with just the four familiar dimensions. We investigate how several upcoming astrophysical experiments will be observationally exploring the possible existence of such axions over a vast mass range from ${10}^{-33}\mathrm{eV}$ to ${10}^{-10}\mathrm{eV}$. Axions with masses between ${10}^{-33}\mathrm{eV}$ to ${10}^{-28}\mathrm{eV}$ can cause a rotation of the cosmic microwave background polarization that is constant throughout the sky. The predicted rotation angle is independent of the scale of inflation and the axion decay constant, and is of order $\alpha \sim 1/137$ –within reach of the just launched Planck satellite. Axions in the mass range ${10}^{-28}\mathrm{eV}$ to ${10}^{-18}\mathrm{eV}$ give rise to multiple steps in the matter power spectrum, providing us with a snapshot of the axiverse that will be probed by galaxy surveys–such as BOSS, and 21 cm line tomography. Axions in the mass range ${10}^{-22}\mathrm{eV}$ to ${10}^{-10}\mathrm{eV}$ can affect the dynamics and gravitational wave emission of rapidly rotating astrophysical black holes through the Penrose superradiance process. When the axion Compton wavelength is of order of the black hole size, the axions develop superradiant atomic bound states around the black hole nucleus. Their occupation number grows exponentially by extracting rotational energy and angular momentum from the ergosphere, culminating in a rotating Bose-Einstein axion condensate emitting gravitational waves. For black holes lighter than $\sim {10}^7$ solar masses accretion cannot replenish the spin of the black hole, creating mass gaps in the spectrum of rapidly rotating black holes that diagnose the presence of destabilizing axions. In particular, the highly rotating black hole in the X-ray binary LMC X-1 implies an upper limit on the decay constant of the QCD axion $f_a\lesssim 2\times {10}^{17}\mathrm{GeV}$, much below the Planck mass. This reach can be improved down to the grand unification scale $f_a\lesssim 2\times {10}^{16}\mathrm{GeV}$, by observing smaller stellar mass black holes.

The potential of the LHC for investigation of anomalous top quark interactions with gluon $(tug,tcg)$ through the production of $tW$ channel of single top quarks is studied. In the standard model, the single top quarks in the $tW$-channel mode are charge symmetric, meaning that $\sigma (pp\to t+W^{-})=\sigma (pp\to \overline{t}+W^{+})$. However, the presence of anomalous flavor-changing neutral current (FCNC) couplings leads to charge asymmetry. In this paper, a method is proposed in which this charge asymmetry may be used to constrain anomalous FCNC couplings. The strength of resulting constraints is estimated for the LHC for the center of mass energies of 7 and 14 TeV.

We compute the top quark decay rate in the unHiggs model. In this model, the longitudinally polarized $W$’s are unparticles, which is owed to their Goldstone boson nature, while the transversely polarized $W$’s are not. Thus the fraction of decays with a longitudinal $W$ emitted is different than in the standard model. Comparing this calculation to CDF data, we are able to rule out some of the unHiggs model parameter space. We also use the expected increased accuracy of top decay measurements at the LHC to anticipate further constraints on the unHiggs.

We extend our work on QCD thermodynamics with $2+1$ quark flavors at nonzero chemical potential to finer lattices with $N_t=6$. We study the equation of state and other thermodynamic quantities, such as quark number densities and susceptibilities, and compare them with our previous results at $N_t=4$. We also calculate the effects of the addition of the charm and bottom quarks on the equation of state at zero and nonzero chemical potential. These effects are important for cosmological studies of the early Universe.

Motivated by recent data from CoGeNT and the DAMA annual modulation signal, we discuss collider constraints on the minimal supersymmetric standard model neutralino dark matter with mass in the 5–15 GeV range. The lightest superpartner (LSP) would be a bino with a small Higgsino admixture. Maximization of the dark matter nucleon scattering cross section for such a weakly interacting massive particle requires a light Higgs boson with $\tan \beta$ enhanced couplings. Limits on the invisible width of the $Z$ boson, combined with the rare decays $B^{\pm }\to \tau \nu$, and the ratio $B\to D\tau \nu /B\to D\ell \nu$, constrain cross sections to be below ${\sigma }_n\lesssim 5\times {10}^{-42}{\mathrm{cm}}^2$. This indicates a higher local dark matter density than is usually assumed by a factor of roughly 6 necessary to explain the CoGeNT excess. This scenario also requires a light charged Higgs boson, which can give substantial contributions to rare decays such as $b\to s\gamma$ and $t\to b{H}^{+}$. We also discuss the impact of Tevatron searches for Higgs bosons at large $\tan \beta$.

We present the results of a search for the radiative decay $B\to K{\eta }^{\prime }\gamma$ and find evidence for $B^{+}\to K^{+}{\eta }^{\prime }\gamma$ decays at the 3.3 standard deviation level with a partial branching fraction of $(3.6\pm 1.2\pm 0.4)\times {10}^{-6}$, where the first error is statistical and the second systematic. This measurement is restricted to the region of combined $K{\eta }^{\prime }$ invariant mass less than $3.4\mathrm{GeV}/c^2$. A 90% confidence level upper limit of $6.4\times {10}^{-6}$ is obtained for the partial branching fraction of the decay $B^0\to K^0{\eta }^{\prime }\gamma$ in the same $K{\eta }^{\prime }$ invariant mass region. These results are obtained from a $605{\mathrm{fb}}^{-1}$ data sample containing $657\times {10}^{6}B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Casimir force encodes the structure of the field modes as vacuum fluctuations and so it is sensitive to the extra dimensions of brane worlds. Now, in flat spacetimes of arbitrary dimension the two standard approaches to the Casimir force, Green’s function, and zeta function yield the same result, but for brane world models this was only assumed. In this work we show that both approaches yield the same Casimir force in the case of universal extra dimensions and Randall-Sundrum scenarios with one and two branes added by $p$ compact dimensions. Essentially, the details of the mode eigenfunctions that enter the Casimir force in the Green’s function approach get removed due to their orthogonality relations with a measure involving the right hypervolume of the plates, and this leaves just the contribution coming from the zeta function approach. The present analysis corrects previous results showing a difference between the two approaches for the single brane Randall-Sundrum; this was due to an erroneous hypervolume of the plates introduced by the authors when using the Green’s function. For all the models we discuss here, the resulting Casimir force can be neatly expressed in terms of two four-dimensional Casimir force contributions: one for the massless mode and the other for a tower of massive modes associated with the extra dimensions.

We study a manifestly gauge-invariant set of Schwinger-Dyson equations to determine the nonperturbative dynamics of the gluon and ghost propagators in $d=3$ Yang-Mills theory. The use of the well-known Schwinger mechanism, in the Landau gauge leads to the dynamical generation of a mass for the gauge boson (gluon in $d=3$), which, in turn, gives rise to an infrared finite gluon propagator and ghost dressing function. The propagators obtained from the numerical solution of these nonperturbative equations are in very good agreement with the results of $SU(2)$ lattice simulations.

In recent years, different views on the interpretation of Lorentz covariance of noncommuting coordinates have been discussed. By a general procedure, we construct the minimal canonical central covariantization of the $\kappa$-Minkowski spacetime. Here, undeformed Lorentz covariance is implemented by unitary operators, in the presence of two dimensionful parameters. We then show that, though the usual $\kappa$-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a noncovariant restriction of the covariantized model. We conclude with some general comments on the approach of deformed covariance.

Highly damped quasinormal frequencies are very often of the form ${\omega }_n=(\mathrm{\text{offset}})+in(\mathrm{\text{gap}})$. We investigate the genericity of this phenomenon by considering a model potential that is piecewise Eckart (piecewise Pöschl-Teller), and developing an analytic “quantization condition” for the highly damped quasinormal frequencies. We find that this ${\omega }_n=(\mathrm{\text{offset}})+in(\mathrm{\text{gap}})$ behavior is generic but not universal, with the controlling feature being whether or not the ratio of the rates of exponential falloff in the two asymptotic directions is a rational number. These observations are of direct relevance to any physical situation where highly damped quasinormal modes (damped modes) are important—in particular (but not limited to) to black hole physics, both theoretical and observational.

We study straight vortices with global longitudinal currents in the Bogomolny limit of the Abelian Higgs model with two charged scalar fields. The model possesses global $SU(2)$ and local electromagnetic $U(1)$ symmetries spontaneously broken to a global $U(1)$ group, and corresponds to a semilocal limit of the standard electroweak model. We show that the contribution of the global $SU(2)$ current to the vortex energy is proportional to the total current squared. Locally, these vortices carry also longitudinal electromagnetic currents, while the total electromagnetic current flowing through a transverse section of the vortex is always zero. The vortices with high winding numbers have, in general, a nested pipelike structure. The magnetic field of the vortex is concentrated at a certain distance from the geometric center of the vortex, thus resembling a “pipe.” This magnetic pipe is layered between two electrically charged pipes that carry longitudinal electric currents in opposite directions.

At zero density, the ‘t Hooft large $N_c$ limit often provides some very useful qualitative insights into the nonperturbative physics of QCD. However, it is known that at high densities the ‘t Hooft large $N_c$ world looks very different from the $N_c=3$ world, which is believed to be in a color-superconducting phase at high densities. At large $N_c$, on the other hand, the Deryagin, Grigoriev, and Rubakov instability causes a chiral-density wave phase to dominate over the color-superconducting phase. There is an alternative large $N_c$ limit, with the quarks transforming in the two-index antisymmetric representation of the gauge group, which at $N_c=3$ reduces to QCD but looks quite different at large $N_c$. We show that in this alternative large $N_c$ limit, the Deryagin, Grigoriev, and Rubakov instability does not occur, so that it may be plausible that the ground state of high-density quark matter is a color superconductor even when $N_c$ is large. This revives the hope that a large $N_c$ approximation might be useful for getting some insights into the high-density phenomenology of QCD.

Using simple 6D junction conditions, we describe two surprising geometries. First in a case of transitions between ${\mathrm{dS}}_4\times S_2$ vacua, the $S_2$ can be stretched significantly larger than the vacuum values both before and after the transition. The same mechanism can also lead to “bubble of nothing” geometries.

In the context of a noncommutative model of coordinate coherent states, we present a Schwarzschild-like metric for a Vaidya solution instead of the standard Eddington-Finkelstein metric. This leads to the appearance of an exact ($t-r$) dependent case of the metric. We analyze the resulting metric in three possible causal structures. In this setup, we find a zero remnant mass in the long-time limit, i.e. an instable black hole remnant. We also study the tunneling process across the quantum horizon of such a Vaidya black hole. The tunneling probability including the time-dependent part is obtained by using the tunneling method proposed by Parikh and Wilczek in terms of the noncommutative parameter $\sigma$. After that, we calculate the entropy associated to this noncommutative black hole solution. However, the corrections are fundamentally trifling; one could respect this as a consequence of quantum inspection at the level of semiclassical quantum gravity.

In this paper we apply to gravitational waves (GW) from the inspiral phase of binary systems a recently derived frequentist methodology to calculate analytically the error for a maximum likelihood estimate of physical parameters. We use expansions of the covariance and the bias of a maximum likelihood estimate in terms of inverse powers of the signal-to-noise ration (SNR)s where the square root of the first order in the covariance expansion is the Cramer Rao lower bound (CRLB). We evaluate the expansions, for the first time, for GW signals in noises of GW interferometers. The examples are limited to a single, optimally oriented, interferometer. We also compare the error estimates using the first two orders of the expansions with existing numerical Monte Carlo simulations. The first two orders of the covariance allow us to get error predictions closer to what is observed in numerical simulations than the CRLB. The methodology also predicts a necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties, SNR, dimension of the parameter space and estimation errors. For example the timing match filtering can achieve the CRLB only if the SNR is larger than the Kurtosis of the gravitational wave spectrum and the necessary SNR is much larger if other physical parameters are also unknown.