We demonstrate that in unquenched quantum electrodynamics (QED), chiral symmetry breaking ceases to exist above a critical number of fermion flavors $N_f$. This is a necessary and sufficient consequence of the fact that there exists a critical value of electromagnetic coupling $\alpha$ beyond which dynamical mass generation gets triggered. We employ a multiplicatively renormalizable photon propagator involving leading logarithms to all orders in $\alpha$ to illustrate this. We study the flavor and coupling dependence of the dynamically generated mass analytically as well as numerically. We also derive the scaling laws for the dynamical mass as a function of $\alpha$ and $N_f$. Up to a multiplicative constant, these scaling laws are related through $(\alpha ,{\alpha }_c)\leftrightarrow (1/N_f,1/N_f^c)$. Calculation of the mass anomalous dimension ${\gamma }_m$ shows that it is always greater than its value in the quenched case. We also evaluate the $\beta$ function. The criticality plane is drawn in the $(\alpha ,N_f)$ phase space which clearly depicts how larger $N_f$ is required to restore chiral symmetry for an increasing interaction strength.

We discuss the phase structure of dense matter, in particular, the nature of the transition between hadronic and quark matter. Calculations within a Ginzburg-Landau approach show that the axial anomaly can induce a critical point in this transition region. This is possible because in three-flavor quark matter with instanton effects a chiral condensate can be added to the color-flavor locked phase without changing the symmetries of the ground state. In (massless) two-flavor quark matter such a critical point is not possible since the corresponding color superconductor (2SC) does not break chiral symmetry. We study the effects of a nonzero but finite strange quark mass which interpolates between these two cases. Since at ultrahigh density the first reaction of the color-flavor locked phase to a nonzero strange quark mass is to develop a kaon condensate, we extend previous Ginzburg-Landau studies by including such a condensate. We discuss the fate of the critical point systematically and show that the continuity between hadronic and quark matter can be disrupted by the onset of a kaon condensate. Moreover, we identify the mass terms in the Ginzburg-Landau potential which are needed for the 2SC phase to occur in the phase diagram.

In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac’s methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green’s functions and a discussion about the obtained results are presented.

We study the motion of spinning test bodies in the de Sitter spacetime of constant positive curvature. With the help of the 10 Killing vectors, we derive the 4-momentum and the tensor of spin explicitly in terms of the spacetime coordinates. However, in order to find the actual trajectories, one needs to impose the so-called supplementary condition. We discuss the dynamics of spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.

We explore the precision with which the Einstein Telescope will be able to measure the parameters of intermediate-mass-ratio inspirals, i.e., the inspirals of stellar mass compact objects into intermediate-mass black holes (IMBHs). We calculate the parameter estimation errors using the Fisher Matrix formalism and present results of Monte Carlo simulations of these errors over choices for the extrinsic parameters of the source. These results are obtained using two different models for the gravitational waveform which were introduced in paper I of this series. These two waveform models include the inspiral, merger, and ringdown phases in a consistent way. One of the models, based on the transition scheme of Ori and Thorne [A. Ori and K. S. Thorne, Phys. Rev. D 62, 124022 (2000).], is valid for IMBHs of arbitrary spin; whereas, the second model, based on the effective-one-body approach, has been developed to cross-check our results in the nonspinning limit. In paper I of this series, we demonstrated the excellent agreement in both phase and amplitude between these two models for nonspinning black holes, and that their predictions for signal-to-noise ratios are consistent to within 10%. We now use these waveform models to estimate parameter estimation errors for binary systems with masses $1.4M_{\odot }+100M_{\odot }$, $10M_{\odot }+100M_{\odot }$, $1.4M_{\odot }+500M_{\odot }$, and $10M_{\odot }+500M_{\odot }$ and various choices for the spin of the central IMBH. Assuming a detector network of three Einstein Telescopes, the analysis shows that for a $10M_{\odot }$ compact object inspiralling into a $100M_{\odot }$ IMBH with spin $q=0.3$, detected with a signal-to-noise ratio of 30, we should be able to determine the compact object and IMBH masses, and the IMBH spin magnitude to fractional accuracies of $\sim {10}^{-3}$, $\sim {10}^{-3.5}$, and $\sim {10}^{-3}$, respectively. We also expect to determine the location of the source in the sky and the luminosity distance to within $\sim 0.003$ steradians and $\sim 10\%$, respectively. We also compute results for several different possible configurations of the detector network to assess how the precision of parameter determination depends on the network configuration.

The Einstein Telescope (ET) is a proposed third-generation ground-based interferometric gravitational wave detector, for which the target is a sensitivity that is a factor of 10 better than Advanced LIGO and a frequency range that extends down to $\sim 1\mathrm{Hz}$. Such a third-generation interferometer will provide opportunities to test Einstein’s theory of relativity in the strong field and will realize precision gravitational wave astronomy with a thousandfold increase in the expected number of events over the advanced ground-based detectors. A design study for ET is currently underway, so it is timely to assess the science that could be done with such an instrument. This paper is the first in a series that will carry out a detailed study of intermediate-mass-ratio inspirals (IMRIs) for ET. In the context of ET, an IMRI is the inspiral of a neutron star or stellar-mass black hole into an intermediate mass black hole (IMBH). In this paper we focus on the development of IMRI waveform models for circular and equatorial inspirals. We consider two approximations for the waveforms, which both incorporate the inspiral, merger, and ringdown phases in a consistent way. One approximation, valid for IMBHs of arbitrary spin, uses the transition model of Ori and Thorne [A. Ori and K. S. Thorne, Phys. Rev. D 62, 124022 (2000).] to describe the merger, and this is then matched smoothly onto a ringdown waveform. The second approximation uses the effective one body approach to model the merger phase of the waveform and is valid for nonspinning IMBHs. In this paper, we use both waveform models to compute signal-to-noise ratios for IMRI sources detectable by ET. At a redshift of $z=1$, we find typical signal-to-noise ratios for IMRI systems with masses $1.4M_{\odot }+100M_{\odot }$, $10M_{\odot }+100M_{\odot }$, $1.4M_{\odot }+500M_{\odot }$ and $10M_{\odot }+500M_{\odot }$ of $\sim 10–25$, $\sim 40–80$, $\sim 3–15$, and $\sim 10–60$, respectively. We also find that the two models make predictions for nonspinning inspirals that are consistent to about 10%.

We carry out a systematic classification and computation of next-to-leading order kinematic power corrections to the fully differential cross section in the parton shower. To do this we devise a map between ingredients in a parton shower and operators in a traditional effective field theory framework using a chain of soft-collinear effective theories. Our approach overcomes several difficulties including avoiding double counting and distinguishing approximations that are coordinate choices from true power corrections. Branching corrections can be classified as hard-scattering, that occur near the top of the shower, and jet-structure, that can occur at any point inside it. Hard-scattering corrections include matrix elements with additional hard partons, as well as power suppressed contributions to the branching for the leading jet. Jet-structure corrections require simultaneous consideration of potential $1\to 2$ and $1\to 3$ branchings. The interference structure induced by collinear terms with subleading powers remains localized in the shower.

Recent years have witnessed tremendous progress in numerical relativity and an ever improving performance of ground-based interferometric gravitational wave detectors. In preparation for the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO) and a new era in gravitational wave astronomy, the numerical relativity and gravitational wave data analysis communities are collaborating to ascertain the most useful role for numerical relativity waveforms in the detection and characterization of binary black hole coalescences. In this paper, we explore the detectability of equal mass, merging black hole binaries with precessing spins and total mass $M_T\in [80,350]M_{\odot }$, using numerical relativity waveforms and templateless search algorithms designed for gravitational wave bursts. In particular, we present a systematic study using waveforms produced by the MayaKranc code that are added to colored, Gaussian noise and analyzed with the Omega burst search algorithm. Detection efficiency is weighed against the orientation of one of the black-hole’s spin axes. We find a strong correlation between the detection efficiency and the radiated energy and angular momentum, and that the inclusion of the $\ell =2$, $m=\pm 1$, 0 modes, at a minimum, is necessary to account for the full dynamics of precessing systems.

We consider the signatures of a domain wall produced in the spontaneous symmetry breaking involving a dilatonlike scalar field coupled to electromagnetism. Domains on either side of the wall exhibit slight differences in their respective values of the fine-structure constant, $\alpha$. If such a wall is present within our Hubble volume, absorption spectra at large redshifts may or may not provide a variation in $\alpha$ relative to the terrestrial value, depending on our relative position with respect to the wall. This wall could resolve the contradiction between claims of a variation of $\alpha$ based on Keck/Hires data and of the constancy of $\alpha$ based on Very Large Telescope data. We derive the properties of the wall and the parameters of the underlying microscopic model required to reproduce the possible spatial variation of $\alpha$. We discuss the constraints on the existence of the low-energy domain wall and describe its observational implications concerning the variation of the fundamental constants.

We analyze quartic gauge-invariant interactions of massless higher spin fields by using vertex operators constructed in our previous works and computing their 4-point amplitudes in superstring theory. The kinematic part of the quartic interactions of the higher spins is determined by the matter structure of their vertex operators; the nonlocality of the interactions is the consequence of the specific ghost structure of these operators. We compute explicitly the 4-point amplitude describing the complete gauge-invariant $1-1-3-3$ quartic interaction (two massless spin 3 particles interacting with two photons) and comment on more general $1-1-s-s$ cases, particularly pointing out the structure of $1-1-5-5$ coupling.

In this paper, we mainly investigate the problems of resonances of massive Kaluza-Klein (KK) fermions on a single scalar constructed thick brane with a piecewise warp factor matching smoothly. The distance between two boundaries and the other parameters are determined by one free parameter through three junction conditions. For the generalized Yukawa coupling $\eta \overline{\Psi }{\varphi }^k\Psi$ with odd $k=1,3,5,\dots$, the mass eigenvalue $m$, width $\Gamma$, lifetime $\tau$, and maximal probability $P_{\max }$ of fermion resonances are obtained. Our numerical calculations show that the brane without internal structure also favors the appearance of resonant states for both left- and right-handed fermions. The scalar-fermion coupling and the thickness of the brane influence the resonant behaviors of the massive KK fermions.

We examine the generation of primordial perturbations during an inflationary epoch in generalized theories of gravity when the equations of motion are derived using the Palatini variational principle. Both $f(R)$ and scalar-tensor theories are considered, and we compare our results with those obtained under the conventional metric formalism. Nonlinear generalizations of the action lead to different theories under the two variational choices, and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result: Inflation driven solely by $f(R)$ modifications does not result in suitable curvature perturbations, while scalar-tensor theories generate nearly scalar invariant curvature perturbations but no tensor modes.

We study head-on collisions of unequal mass black hole binaries in $D=5$ spacetime dimensions, with mass ratios between $1\mathrm{\text{:}}1$ and $1\mathrm{\text{:}}4$. Information about gravitational radiation is extracted by using the Kodama-Ishibashi gauge-invariant formalism and details of the apparent horizon of the final black hole. We present waveforms, total integrated energy and momentum for this process. Our results show surprisingly good agreement, within 5% or less, with those extrapolated from linearized, point-particle calculations. Our results also show that consistency with the area theorem bound requires that the same process in a large number of spacetime dimensions must display new features.

We consider a novel class of $f(\mathcal{R})$ gravity theories where the connection is related to the conformally scaled metric ${\widehat{g}}_{\mu \nu }=C(\mathcal{R})g_{\mu \nu }$ with a scaling that depends on the scalar curvature $\mathcal{R}$ only. We call them $C$ theories and show that the Einstein and Palatini gravities can be obtained as special limits. In addition, $C$ theories include completely new physically distinct gravity theories even when $f(\mathcal{R})=\mathcal{R}$. With nonlinear $f(\mathcal{R})$, $C$ theories interpolate and extrapolate the Einstein and Palatini cases and may avoid some of their conceptual and observational problems. We further show that $C$ theories have a scalar-tensor formulation, which in some special cases reduces to simple Brans-Dicke–type gravity. If matter fields couple to the connection, the conservation laws in $C$ theories are modified. The stability of perturbations about flat space is determined by a simple condition on the Lagrangian.

In dimension 2 and above, the Burgers dynamics, the so-called “adhesion model” in cosmology, can actually give rise to several dynamics in the inviscid limit. We investigate here the statistical properties of the density field when it is defined by a “geometrical model” associated with this Burgers velocity field and where the matter distribution is fully determined, at each time step, by geometrical constructions. Our investigations are based on a set of numerical experiments that make use of an improved algorithm, for which the geometrical constructions are efficient and robust. In this work we focus on Gaussian initial conditions with power-law power spectra of slope $n$ in the range $-3<n<1$, where a self-similar evolution develops, and we compute the behavior of power spectra, density probability distributions and mass functions. As expected for such dynamics, the density power spectra show universal high-$k$ tails that are governed by the formation of pointlike masses. The two other statistical indicators however show the same qualitative properties as those observed for 3D gravitational clustering. In particular, the mass functions obey a Press-Schechter like scaling up to a very good accuracy in 1D, and to a lesser extent in 2D. Our results suggest that the “geometrical adhesion model,” whose solution is fully known at all times, provides a precious tool to understand some of the statistical constructions frequently used to study the development of mass halos in gravitational clustering.

We describe a way to construct supergravity models with an arbitrary inflaton potential $V(\varphi )$ and show that all other scalar fields in this class of models can be stabilized at the inflationary trajectory by a proper choice of the Kähler potential.

After constructing all the tetraquark interpolating currents with $J^{\mathrm{PC}}=1^{-+}$, $1^{--}$, $1^{++}$ and $1^{+-}$ in a systematic way, we investigate the two-point correlation functions to extract the masses of the charmoniumlike states with QCD sum rule. For the $1^{--}$ $qc\overline{q}\overline{c}$ charmoniumlike state, $m_X=4.6\sim 4.7\mathrm{GeV}$, which implies a possible tetraquark interpretation for the state $Y(4660)$. The masses for both the $1^{++}$ $qc\overline{q}\overline{c}$ and $sc\overline{s}\overline{c}$ charmoniumlike states are around $4.0\sim 4.2\mathrm{GeV}$, which are slightly above the mass of $X(3872)$. For the $1^{-+}$ and $1^{+-}$ $qc\overline{q}\overline{c}$ charmoniumlike states, the extracted masses are around $4.5\sim 4.7\mathrm{GeV}$ and $4.0\sim 4.2\mathrm{GeV}$, respectively. As a by-product, the bottomoniumlike states are also studied. We also discuss the possible decay modes and experimental search of the charmoniumlike states.

We discuss how the angular distribution of lepton pairs from decays of vector mesons depends on the choice of reference frame, and provide a geometrical description of the transformations of the coefficients of the angular distribution. Invariant expressions involving all coefficients are discussed, together with bounds and consistency relations.

We use gauge theory/string theory correspondence to study finite temperature critical behavior of mass-deformed $\mathcal{N}=4$ $SU(N)$ supersymmetric Yang-Mills theory at strong coupling, also known as $\mathcal{N}=2^{*}$ gauge theory. For a certain range of the mass parameters, $\mathcal{N}=2^{*}$ plasma undergoes a second-order phase transition. We compute all the static critical exponents of the model and demonstrate that the transition is of the mean-field theory type. We show that the dynamical critical exponent of the model is $z=0$, with multiple hydrodynamic relaxation rates at criticality. We point out that the dynamical critical phenomena in $\mathcal{N}=2^{*}$ plasma is outside the dynamical universality classes established by Hohenberg and Halperin.