Explicit analytical expressions are derived for the gluon propagator in a generic linear covariant $R_{\xi }$ gauge, by a screened massive expansion for the exact Faddeev-Popov Lagrangian of pure Yang-Mills theory. At one-loop, if the gauge invariance of the pole structure is enforced, the gluon dressing function is entirely and uniquely determined, without any free parameter or external input. The gluon propagator is found finite in the IR for any $\xi$, with a slight decrease of its limit value when going from the Landau gauge ($\xi =0$) toward the Feynman gauge ($\xi =1$). An excellent agreement is found with the lattice in the range $0<\xi <0.5$ where the data are available.

We propose a partonic picture for high-mass diffractive dissociation events in onium-nucleus scattering, which leads to simple and robust predictions for the distribution of the sizes of gaps in diffractive dissociation of virtual photons off nuclei at very high energies. We show that the obtained probability distribution can formally be identified to the distribution of the decay time of the most recent common ancestor of a set of objects generated near the edge of a branching random walk, and explain the physical origin of this appealing correspondence. We then use the fact that the diffractive cross section conditioned to a minimum rapidity gap size obeys a set of Balitsky-Kovchegov equations in order to test numerically our analytical predictions. Furthermore, we show how simulations in the framework of a Monte Carlo implementation of the QCD evolution support our picture.

We show that the high-temperature limits of the heterotic $E_8\times E_8$ and $\mathrm{Spin}32/\mathrm{Z}2$ strings and their type I A/B superstring duals are finite and convergent. The Hagedorn growth of the degeneracies in the string mass level expansion is suppressed by an exponential that is linear in the mass level number for both heterotic strings, and suppressed by the exponential of the negative square root of the mass level number for the type IB superstring. However, in the massless gauge field-theoretic limit of the type IB open and closed superstring, we find clear evidence for the thermal deconfinement phase transition at the self-dual temperature by examining the annulus graph alone. Above the self-dual temperature, there is a discontinuity in the first derivative with respect to temperature of both the free energy, and the heavy quark potential, leading to a deconfined thermal gluon ensemble, with universal $1/r$ potential, and temperature-dependent corrections, as predicted by Lüscher and Weisz. A number of essential aspects of the worldsheet formalism of the heterotic strings are derived in an Appendix, deducing thereby the O8-D0-D8-brane type IA duals of all of the heterotic Chaudhuri-Hockney-Lykken island universe moduli spaces.

We study a complex free scalar field theory on a noncommutative background spacetime called $\kappa$-Minkowski. We ensure the Lorentz invariance of the theory by assuming an “elliptic de Sitter” topology for momentum space. To define covariant quantization rules, we introduce a noncommutative Pauli-Jordan function, which is invariant under $\kappa$-deformed Poincaré transformations, as well as diffeomorphisms of momentum space. We derive the algebra of creation and annihilation operators implied by our Pauli-Jordan function. Finally, we use our construction to study the structure of the light cone in $\kappa$-Minkowski spacetime, and to derive its physical consequences.

We analyze the pair production induced by homogenous, time-dependent electric fields in an expanding space-time background. We point out that, in obtaining the semiclassical Maxwell equations, two distinct notions of adiabatic renormalization are possible. In Minkowski space, the two recipes turn out to be equivalent. However, in the presence of gravity, only the recipe requiring an adiabatic hierarchy between the gravitational and the gauge field is consistent with the conservation of the energy-momentum tensor.

We study the quasinormal modes for scalar, axial and radial perturbations of massive static spherically symmetric wormholes supported by a phantom scalar field, calculating the modes directly and employing the WKB approximation. The spectrum of the quasinormal modes is compared with the spectrum of Schwarzschild black holes. For fixed multipole number $l$ and large mass $M$ the wormhole modes approach their black hole counterparts as $1/M$.

Dwarf spheroidal galaxies are among the most promising targets for indirect dark matter (DM) searches in $\gamma$ rays. The $\gamma$-ray flux from DM annihilation in a dwarf spheroidal galaxy is proportional to the $J$-factor of the source. The $J$-factor of a dwarf spheroidal galaxy is the line-of-sight integral of the DM mass density squared times $⟨{\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}⟩/({\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}{)}_0$, where ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$ is the DM annihilation cross-section times relative velocity $v_{\mathrm{rel}}=|{\mathit{v}}_{\mathrm{rel}}|$, angle brackets denote average over ${\mathit{v}}_{\mathrm{rel}}$, and $({\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}{)}_0$ is the $v_{\mathrm{rel}}$-independent part of ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$. If ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$ is constant in $v_{\mathrm{rel}}$, $J$-factors only depend on the DM space distribution in the source. However, if ${\sigma }_{\mathrm{ann}}{v}_{\mathrm{rel}}$ varies with $v_{\mathrm{rel}}$, as in the presence of DM self-interactions, $J$-factors also depend on the DM velocity distribution, and on the strength and range of the DM self-interaction. Models for self-interacting DM are increasingly important in the study of the small scale clustering of DM, and are compatible with current astronomical and cosmological observations. Here we derive the $J$-factor of 20 dwarf spheroidal galaxies from stellar kinematic data under the assumption of Yukawa DM self-interactions. $J$-factors are derived through a profile likelihood approach, assuming either Navarro-Frenk-White (NFW) or cored DM profiles. We also compare our results with $J$-factors derived assuming the same velocity for all DM particles in the target galaxy. We find that this common approximation overestimates the $J$-factors by up to 1 order of magnitude. $J$-factors for a sample of DM particle masses and self-interaction coupling constants, as well as for NFW and cored density profiles, are provided electronically, ready to be used in other projects.

Ensembles of magnetic defects represent quantum variables that have been detected and extensively explored in lattice $\mathrm{SU}(N)$ pure Yang-Mills theory. They successfully explain many properties of confinement and are strongly believed to capture the (infrared) path-integral measure. In this work, we initially motivate the presence of magnetic non-Abelian degrees of freedom in these ensembles. Next, we consider a simple Gaussian model to account for fluctuations. In this case, both center vortices and monopoles become relevant degrees in Wilson loop averages. These physical inputs are then implemented in an ensemble of percolating center vortices in four dimensions by proposing a measure to compute center-element averages. The introduction of phenomenological information such as monopole tension, stiffness, and fusion leads to an effective YMH model with adjoint Higgs fields. If monopoles also condense, then the gauge group undergoes $\mathrm{SU}(N)\to \mathrm{Z}(N)$ SSB. This pattern has been proposed as a strong candidate to describe confinement. In the presence of external quarks, these models are known to be dominated by classical solutions, formed by flux tubes with $N$-ality as well as by confined dual monopoles (gluons).

The instant form and the front form of relativistic dynamics proposed by Dirac in 1949 can be linked by an interpolation angle parameter $\delta$ spanning between the instant form dynamics (IFD) at $\delta =0$ and the front form dynamics, which is now known as the light-front dynamics (LFD) at $\delta =\pi /4$. We present the formal derivation of the interpolating quantum electrodynamics (QED) in the canonical field theory approach and discuss the constraint fermion degree of freedom, which appears uniquely in the LFD. The constraint component of the fermion degrees of freedom in LFD results in the instantaneous contribution to the fermion propagator, which is genuinely distinguished from the ordinary equal-time forward and backward propagation of relativistic fermion degrees of freedom. As discussed recently, the helicity of the on-mass-shell fermion spinors in LFD is also distinguished from the ordinary Jacob-Wick helicity in the IFD with respect to whether the helicity depends on the reference frame or not. To exemplify the characteristic difference of the fermion propagator between IFD and LFD, we compute the helicity amplitudes of typical QED processes such as $e^{+}{e}^{-}\to \gamma \gamma$ and $e\gamma \to e\gamma$ and present the whole landscape of the scattering amplitudes in terms of the frame dependence or the scattering angle dependence with respect to the interpolating angle dependence. Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the infinite momentum frame approach and the LFD.

We consider electroweak Higgs plus three jets production at NLO QCD beyond strict VBF acceptance cuts. We investigate, for the first time, how accurate the VBF approximation is in these regions and within perturbative uncertainties by a detailed comparison of full and approximate calculations. We find that a rapidity gap between the tagging jets guarantees a good approximation, while an invariant mass cut alone is not sufficient, which needs to be confronted with experimental choices. We also find that a significant part of the QCD corrections can be attributed to Higgs-Strahlungs-type topologies.

We present the construction of a new family of coherent states for quantum theories of connections obtained following the polymer quantization. The realization of these coherent states is based on the notion of graph change, in particular the one induced by the quantum dynamics in Yang-Mills and gravity quantum theories. Using a Fock-like canonical structure that we introduce, we derive the new coherent states that we call the graph coherent states. These states take the form of an infinite superposition of basis network states with different graphs. We further discuss the properties of such states and certain extensions of the proposed construction.

The two $LAGEOS$ and $LARES$ are laser-ranged satellites tracked with the best accuracy ever achieved. Using their range measurements many geophysical parameters were calculated and some general relativity effects were directly observed. To obtain precise and refined measurements of the effects due to the predictions of general relativity on the orbit of these satellites, it is mandatory to model with high precision and accuracy all other forces, reducing the free parameters introduced in the orbit determination. A main category of nongravitational forces to be considered are those of thermal origin, whose fine modeling strongly depends on the knowledge of the evolution of the spin vector. We present a complete model, named LASSOS, to describe the evolution of the spin of the $LAGEOS$ and $LARES$ satellites. In particular, we solved Euler equations of motion considering not-averaged torques. This is the most general case, and the predictions of the model well fit the available observations of the satellites spin. We also present the predictions of our model in the fast-spin limit, based on the application of averaged equations. The results are in good agreement with those already published, but with our approach we have been able to highlight small errors within these previous works. LASSOS was developed within the LARASE research program. LARASE aims to improve the dynamical model of the two $LAGEOS$ and $LARES$ satellites to provide very precise and accurate measurements of relativistic effects on their orbit, and also to bring benefits to geophysics and space geodesy.

In this paper, using the recent method proposed by Ono, Ishihara and Asada (OIA) who extend the idea of Gibbons and Werner to the stationary and axisymmetric case, we apply the Gauss-Bonnet theorem to the optical metric of the non-rotating and rotating Damour-Solodukhin wormholes spacetimes to study the weak gravitational lensing by these objects. Furthermore, we study the strong gravitational lensing by the nonrotating Damour-Solodukhin wormholes using the Bozza’s method to see the differences between the weak lensing and the strong lensing. We demonstrate the relation between the strong deflection angle and quasinormal modes of the Damour-Solodukhin wormholes. Interestingly it is found that the wormhole parameter $\lambda$, affects the deflection of light in strong and weak limits compared to the previous studies of gravitational lensing by Schwarzschild black holes. Hence, the results provide a unique tool to shed light on the possible existence of wormholes.

In this paper we show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid manifold whose geometry we construct explicitly. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form. As a consequence we can show how the Einstein-Hilbert, Gauss-Bonnet and, in general, the Euler scalar densities can be written as the divergences of genuine vector densities in the critical dimensions $D=2$, 4, etc. As Lovelock gravity is a dimensional continuation of Euler densities, these results are of relevance for Gauss-Bonnet and, in general, Lovelock gravity. Indeed, these vectors which can be called generalized Katz vectors ensure, in particular, a well-defined variational principle with Dirichlet boundary conditions.

Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a nontrivial Killing tensor, we fully integrate Einstein’s vacuum equation with a cosmological constant. Although most of the solutions happen to be already known, we have found a solution that, as far as we could search for, has not been attained before. We also characterize the geometric properties of this new solution, it is a Kundt spacetime of Petrov type II possessing a null Killing vector field and an isometry algebra that is three-dimensional and Abelian. In particular, such solution becomes a $pp$-wave spacetime when the cosmological constant is set to zero.

While a fully coherent all-sky search is known to be optimal for detecting signals from compact binary coalescences (CBCs), its high computational cost has limited current searches to less sensitive coincidence-based schemes. For a network of first-generation GW detectors, it has been demonstrated that particle swarm optimization (PSO) can reduce the computational cost of this search, in terms of the number of likelihood evaluations, by a factor of $\approx 10$ compared to a grid-based optimizer. Here, we extend the PSO-based search to a network of second-generation detectors and present further substantial improvements in its performance by adopting the local-best variant of PSO and an effective strategy for tuning its configuration parameters. It is shown that a PSO-based search is viable over the entire binary mass range relevant to second-generation detectors at realistic signal strengths.

Characterizing the properties of black holes is one of the most important science objectives for gravitational-wave observations. Astrophysical evidence suggests that black holes that are nearly extremal (i.e., spins near the theoretical upper limit) might exist and, thus, might be among the merging black holes observed with gravitational waves. In this paper, we explore how well current gravitational wave parameter estimation methods can measure the spins of rapidly spinning black holes in binaries. We simulate gravitational-wave signals using numerical-relativity waveforms for nearly-extremal, merging black holes. For simplicity, we confine our attention to binaries with spins parallel or antiparallel with the orbital angular momentum. We find that recovering the holes’ nearly extremal spins is challenging. When the spins are nearly extremal and parallel to each other, the resulting parameter estimates do recover spins that are large, though the recovered spin magnitudes are still significantly smaller than the true spin magnitudes. When the spins are nearly extremal and antiparallel to each other, the resulting parameter estimates recover the small effective spin but incorrectly estimate the individual spins as nearly zero. We study the effect of spin priors and argue that a commonly used prior (uniform in spin magnitude and direction) hinders unbiased recovery of large black-hole spins.

We systematically study the preinflationary dynamics of the spatially flat Friedmann-Lemaitre-Robertson-Walker universe filled with a single scalar field that has the generalized $\alpha$-attractor potentials, in the framework of loop quantum cosmology, in which the big bang singularity is replaced generically by a nonsingular quantum bounce due to purely quantum geometric effects. The evolution can be divided into two different classes, one is dominated initially (at the quantum bounce) by the kinetic energy of the scalar field, and one is not. In both cases, we identify numerically the physically viable initial conditions that lead to not only a slow-roll inflationary phase, but also enough $e$-folds to be consistent with observations, and find that the output of such a viable slow-roll inflationary phase is generic. In addition, we also show that in the case when the evolution of the universe is dominated initially by the kinetic energy of the scalar field (except for a very small set in the phase space), the evolution before reheating is always divided into three different phases: bouncing, transition and slow-roll inflation. This universal feature does not depend on the initial conditions of the system nor on the specific potentials of the scalar field, as long as it is dominated initially by the kinetic energy of the scalar field at the bounce. Moreover, we carry out phase space analyses for the models under consideration and compare our results with the power-law and Starobinsky potentials.

The so-called trans-Planckian problem of inflation may be evaded by positing that modes come into existence only when they became “cis-Planckian” by virtue of expansion. However, this would imply that for any mode a new random realization would have to be drawn every $N$ wavelengths, with $N$ typically of order 1000 (but it could be larger or smaller). Such a redrawing of realizations leads to a heteroskodastic distribution if the region under observation contains several such independent domains. This has no effect on the sampled power spectrum for a scale-invariant raw spectrum, but at very small scales, it leads to a spectral index bias toward scale invariance and smooths oscillations in the spectrum. The domain structure would also “unsqueeze” some of the propagating waves, i.e., dismantle their standing wave character. By describing standing waves as traveling waves of the same amplitude moving in opposite directions, we determine the observational effects of unsqueezing. We find that it would erase the Doppler peaks in the cosmic microwave background, but only on very small angular scales, in which the primordial signal may not be readily accessible. The standing waves in a primordial gravitational wave background would also be turned into traveling waves. This unsqueezing of the gravitational wave background may constitute a detectable phenomenon.