We investigate the perturbative expansion in $SU(3)$ Yang-Mills theory compactified on ${\mathbb{R}}^2\times {\mathbb{T}}^2$ where the compact space is a torus ${\mathbb{T}}^2=S_{\beta }^1\times S_L^1$, with $S_{\beta }^1$ being a thermal circle with period $\beta =1/T$ ($T$ is the temperature) while $S_L^1$ is a circle with finite length $L=1/M$, where $M$ is an energy scale. A Linde-type analysis indicates that perturbative calculations for the pressure in this theory break down already at order $\mathcal{O}(g^2)$ due to the presence of a nonperturbative scale $\sim g\sqrt{TM}$. We conjecture that a similar result should hold if the torus is replaced by any other compact surface of genus one.

In the Standard Model of electroweak interactions and in the tree approximation we calculate the rate and branching ratio of the neutron radiative ${\beta }^{-}$ decay with one real photon emission by taking into account the contributions of the weak magnetism and proton recoil to order $1/m_p$ of the large proton mass $m_p$ expansion. We find that the obtained contributions of the weak magnetism and proton recoil increase the rate and branching ratio of the neutron radiative ${\beta }^{-}$ decay by about 0.70%. This is large compared with the contribution of the weak magnetism and proton recoil of about 0.16% to the rate of the neutron ${\beta }^{-}$ decay, calculated in Phys. Rev. D 88, 073002 (2013).

The coefficient of the dimensionally regularized two-loop $R^3$ divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.

We compute the polylogarithmic parts of the two-loop four- and five-graviton amplitudes where the external helicities are positive and express these in a simple compact analytic form. We use these to extract the $\ln ({\mu }^2)$ terms from both the four- and five-point amplitudes and show that these match the same $R^3$ counterterm.

Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the non-vacuum Kasner-AdS geometry and its solitonic generalization. To characterize these space-times, we provide ways to embed them in higher dimensional flat space-times. General space-like geodesics are then studied and used to compute the two point boundary correlators within the geodesic approximation.

We compute the finite temperature ghost and gluon propagators of Yang-Mills theory in the Landau-DeWitt gauge. The background field that enters the definition of the latter is intimately related with the (gauge-invariant) Polyakov loop and serves as an equivalent order parameter for the deconfinement transition. We use an effective gauge-fixed description where the nonperturbative infrared dynamics of the theory is parametrized by a gluon mass which, as argued elsewhere, may originate from the Gribov ambiguity. In this scheme, one can perform consistent perturbative calculations down to infrared momenta, which have been shown to correctly describe the phase diagram of Yang-Mills theories in four dimensions as well as the zero-temperature correlators computed in lattice simulations. In this article, we provide the one-loop expressions of the finite temperature Landau-DeWitt ghost and gluon propagators for a large class of gauge groups and present explicit results for the SU(2) case. These are substantially different from those previously obtained in the Landau gauge, which corresponds to a vanishing background field. The nonanalyticity of the order parameter across the transition is directly imprinted onto the propagators in the various color modes. In the SU(2) case, this leads, for instance, to a cusp in the electric and magnetic gluon susceptibilities as well as similar signatures in the ghost sector. We mention the possibility that such distinctive features of the transition could be measured in lattice simulations in the background field gauge studied here.

This paper is focused on the functional renormalization group applied to the $T_5^6$ tensor model on the Abelian group $U(1)$ with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.

We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.

In order to construct a gauge-invariant two-point function in a Yang-Mills theory, we propose the use of the all-order gauge-invariant transverse configurations $A^h$. Such configurations can be obtained through the minimization of the functional $A_{\min }^2$ along the gauge orbit within the BRST-invariant formulation of the Gribov-Zwanziger framework recently put forward in [1,2] for the class of the linear covariant gauges. This correlator turns out to provide a characterization of nonperturbative aspects of the theory in a BRST-invariant and gauge-parameter-independent way. In particular, it turns out that the poles of $⟨A_{\mu }^h(k)A_{\nu }^h(-k)⟩$ are the same as those of the transverse part of the gluon propagator, which are also formally shown to be independent of the gauge parameter $\alpha$ entering the gauge condition through the Nielsen identities. The latter follow from the new exact BRST-invariant formulation introduced before. Moreover, the correlator $⟨A_{\mu }^h(k)A_{\nu }^h(-k)⟩$ enables us to attach a BRST-invariant meaning to the possible positivity violation of the corresponding temporal Schwinger correlator, giving thus for the first time a consistent, gauge parameter independent, setup to adopt the positivity violation of $⟨A_{\mu }^h(k)A_{\nu }^h(-k)⟩$ as a signature for gluon confinement. Finally, in the context of gauge theories supplemented with a fundamental Higgs field, we use $⟨A_{\mu }^h(k)A_{\nu }^h(-k)⟩$ to probe the pole structure of the massive gauge boson in a gauge-invariant fashion.

As time passes, once simple quantum states tend to become more complex. For strongly coupled $k$-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we show that the same pattern is exhibited by a much simpler system—classical geodesics on a compact two-dimensional geometry of uniform negative curvature. This striking parallel persists whether the system is allowed to evolve naturally or is perturbed from the outside.

The pioneering discovery of gravitational waves (GWs) by Advanced LIGO has ushered us into an era of observational GW astrophysics. Compact binaries remain the primary target sources for GW observation, of which neutron star-black hole (NSBH) binaries form an important subset. GWs from NSBH sources carry signatures of (a) the tidal distortion of the neutron star by its companion black hole during inspiral, and (b) its potential tidal disruption near merger. In this paper, we present a Bayesian study of the measurability of neutron star tidal deformability ${\mathrm{\Lambda }}_{\mathrm{NS}}\propto (R/M{)}_{\mathrm{NS}}^5$ using observation(s) of inspiral-merger GW signals from disruptive NSBH coalescences, taking into account the crucial effect of black hole spins. First, we find that if nontidal templates are used to estimate source parameters for an NSBH signal, the bias introduced in the estimation of nontidal physical parameters will only be significant for loud signals with signal-to-noise ratios greater than $\simeq 30$. For similarly loud signals, we also find that we can begin to put interesting constraints on ${\mathrm{\Lambda }}_{\mathrm{NS}}$ (factor of 1–2) with individual observations. Next, we study how a population of realistic NSBH detections will improve our measurement of neutron star tidal deformability. For an astrophysically likely population of disruptive NSBH coalescences, we find that 20–35 events are sufficient to constrain ${\mathrm{\Lambda }}_{\mathrm{NS}}$ within $\pm 25\%–50\%$, depending on the neutron star equation of state. For these calculations we assume that LIGO will detect black holes with masses within the astrophysical mass gap. In case the mass gap remains preserved in NSBHs detected by LIGO, we estimate that approximately 25% additional detections will furnish comparable ${\mathrm{\Lambda }}_{\mathrm{NS}}$ measurement accuracy. In both cases, we find that it is the loudest 5–10 events that provide most of the tidal information, and not the combination of tens of low-SNR events, thereby facilitating targeted numerical-GR follow-ups of NSBHs. We find these results encouraging, and recommend that an effort to measure ${\mathrm{\Lambda }}_{\mathrm{NS}}$ be planned for upcoming NSBH observations with the LIGO-Virgo instruments.

In this work we will test an alternative model of gravity belonging to the large family of Galileon models. It is characterized by an intrinsic breaking of the Vainshtein mechanism inside large astrophysical objects, thus having possibly detectable observational signatures. We will compare theoretical predictions from this model with the observed total mass profile for a sample of clusters of galaxies. The profiles are derived using two complementary tools: x-ray hot intracluster gas dynamics, and strong and weak gravitational lensing. We find that a dependence with the dynamical internal status of each cluster is possible; for those clusters which are very close to be relaxed, and thus less perturbed by possible astrophysical local processes, the Galileon model gives a quite good fit to both x-ray and lensing observations. Both masses and concentrations for the dark matter halos are consistent with earlier results found in numerical simulations and in the literature, and no compelling statistical evidence for a deviation from general relativity is detectable from the present observational state. Actually, the characteristic Galileon parameter $\mathrm{\Upsilon }$ is always consistent with zero, and only an upper limit ($\lesssim 0.086$ at $1\sigma$, $\lesssim 0.16$ at $2\sigma$, and $\lesssim 0.23$ at $3\sigma$) can be established. Some interesting distinctive deviations might be operative, but the statistical validity of the results is far from strong, and better data would be needed in order to either confirm or reject a potential tension with general relativity.

We discuss two spherically symmetric solutions admitted by the Horndeski (or scalar-tensor) theory in the context of Solar System and astrophysical scenarios. One of these solutions is derived for Einstein-Gauss-Bonnet gravity, while the other originates from the coupling of the Gauss-Bonnet invariant with a scalar field. Specifically, we discuss the perihelion precession and the bending angle of light for these two different spherically symmetric spacetimes derived in Maeda and Dadhich [Phys. Rev. D 75, 044007 (2007)] and Sotiriou and Zhou [Phys. Rev. D 90, 124063 (2014)], respectively. The latter, in particular, applies only to black-hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.

We calculate the sensitivity to a circular polarization of an isotropic stochastic gravitational wave background (ISGWB) as a function of frequency for ground- and space-based interferometers and observations of the cosmic microwave background. The origin of a circularly polarized ISGWB may be due to exotic primordial physics (i.e., parity violation in the early universe) and may be strongly frequency dependent. We present calculations within a coherent framework which clarifies the basic requirements for sensitivity to circular polarization, in distinction from previous work which focused on each of these techniques separately. We find that the addition of an interferometer with the sensitivity of the Einstein Telescope in the southern hemisphere improves the sensitivity of the ground-based network to circular polarization by about a factor of two. The sensitivity curves presented in this paper make clear that the wide range in frequencies of current and planned observations (${10}^{-18}\mathrm{Hz}\lesssim f\lesssim 100\mathrm{Hz}$) will be critical to determining the physics that underlies any positive detection of circular polarization in the ISGWB. We also identify a desert in circular polarization sensitivity for frequencies between ${10}^{-15}\mathrm{Hz}\lesssim f\lesssim {10}^{-3}\mathrm{Hz}$, given the inability for pulsar timing arrays and indirect-detection methods to distinguish the gravitational wave polarization.

We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate Friedmann-Robertson-Walker cosmology in their angle average. In order to be able to identify the local volume expansion and curvature in a long-wavelength perturbation with those of the separate universe, we show that the lapse perturbation must be much smaller in amplitude than the curvature potential on a time slicing that comoves with the Einstein tensor. Interpreting the Einstein tensor as an effective stress-energy tensor, the condition is that the effective stress energy comoves with freely falling synchronous observers who establish the local expansion, so that the local curvature is conserved. By matching the expansion history of these synchronous observers in cosmological simulations, one can establish and test consistency relations even in the nonlinear regime of modified gravity theories.

We present an analytic formula for the galaxy bispectrum in redshift space on the basis of the halo approach description with the halo occupation distribution of central galaxies and satellite galaxies. This work is an extension of a previous work on the galaxy power spectrum, which illuminated the significant contribution of satellite galaxies to the higher multipole spectrum through the nonlinear redshift space distortions of their random motions. Behaviors of the multipoles of the bispectrum are compared with results of numerical simulations assuming a halo occupation distribution of the low-redshift (LOWZ) sample of the Sloan Digital Sky Survey (SDSS) III baryon oscillation spectroscopic survey (BOSS) survey. Also presented are analytic approximate formulas for the multipoles of the bispectrum, which is useful to understanding their characteristic properties. We demonstrate that the Fingers of God effect is quite important for the higher multipoles of the bispectrum in redshift space, depending on the halo occupation distribution parameters.

We study cosmological constraints on dark pure Yang-Mills sectors. Dark glueballs are overproduced for large regions of ultraviolet parameter space. The problem may be alleviated in two ways: via a large preferential reheating into the visible sector, motivating certain inflation or modulus decay models, or via decays into axions or moduli, which are strongly constrained by nucleosynthesis and $\mathrm{\Delta }{N}_{\mathrm{eff}}$ bounds. String models frequently have multiple hidden Yang-Mills sectors, which are subject to even stronger constraints due to the existence of multiple dark glueballs.

Dynamical Dark Matter (DDM) is an alternative framework for dark-matter physics in which the dark sector comprises a vast ensemble of particle species whose Standard-Model decay widths are balanced against their cosmological abundances. Previous studies of this framework have focused on a particular class of DDM ensembles—motivated primarily by Kaluza-Klein towers in theories with extra dimensions—in which the density of dark states scales roughly as a polynomial of the mass. In this paper, by contrast, we study the properties of a different class of DDM ensembles in which the density of dark states grows exponentially with mass. Ensembles with this Hagedorn-like property arise naturally as the “hadronic” resonances associated with the confining phase of a strongly-coupled dark sector; they also arise naturally as the gauge-neutral bulk states of Type I string theories. We study the dynamical properties of such ensembles, and demonstrate that an appropriate DDM-like balancing between decay widths and abundances can emerge naturally—even with an exponentially rising density of states. We also study the effective equations of state for such ensembles, and investigate some of the model-independent observational constraints on such ensembles that follow directly from these equations of state. In general, we find that such constraints tend to introduce correlations between various properties of these DDM ensembles such as their associated mass scales, lifetimes, and abundance distributions. For example, we find that these constraints allow DDM ensembles with energy scales ranging from the GeV scale all the way to the Planck scale, but that the total present-day cosmological abundance of the dark sector must be spread across an increasing number of different states in the ensemble as these energy scales are dialed from the Planck scale down to the GeV scale. Numerous other correlations and constraints are also discussed.

We revisit the global dynamics of unified dark matter cosmological models and analyze it in a new dynamical system setting. In particular, by defining a suitable set of variables we obtain a bounded variable space, a feature that allows a better control of the critical elements of the system. First, we give a comprehensive cosmological interpretation of the critical points. Then, we turn our focus on particular representative trajectories with physically motivated initial conditions studied in the first paper of the series, and we discuss how the scale factor relates to the equation of state parameter. We review and complement these results in the light of the new variable approach by discussing the issue of whether the system is chaotic or not.