Hamiltonian renormalization, as defined within this series of works, was derived from covariant Wilson renormalization via Osterwalder-Schrader reconstruction. As such it directly applies to quantum field theory (QFT) with a true (physical) Hamiltonian bounded from below. The validity of the scheme was positively tested for free QFT in any dimension with or without Abelian gauge symmetries of Yang-Mills type. The aim of this Hamiltonian renormalization scheme is to remove quantization ambiguities of Hamiltonians in interacting QFT that remain even after UV and IR regulators are removed as it happens in highly nonlinear QFT such as quantum gravity. Also, while not derived for that case, the renormalization flow formulas can without change also be applied to QFT without a single true Hamiltonian but rather an infinite number of Hamiltonian constraints. In that case a number of interesting questions arise: (1) Does the flow reach the correct fixed point also for an infinite number of “Hamiltonians” simultaneously? (2) As the constraints are labeled by test functions, which in the presence of a regulator are typically regularized (discretized and of compact support), how do those test functions react to the flow? (3) Does the quantum constraint algebra, which in the presence of a regulator is expected to be anomalous, close at the fixed point? These questions should ultimately be addressed in quantum gravity. Before one considers this interacting, constrained QFT, it is well-motivated to consider a free, constrained QFT where the fixed point is explicitly known. In this paper we therefore address the case of parametrized field theory for which the quantum constraint algebra coincides simultaneously with the hypersurface deformation algebra of quantum gravity (or any other generally covariant theory) and the Virasoro algebra of free, closed, bosonic string theory or other conformal field theories to which the results of this paper apply verbatim. The central result of our investigation is that the finite resolution (discretized) constraint algebras typically do not close, that there is not necessarily anything wrong with that, and that anomaly freeness of the continuum algebra is encoded in the convergence behavior of the renormalization flow.

The recent announcement of strong evidence for a stochastic gravitational-wave background (SGWB) by various pulsar timing array collaborations has highlighted this signal as a promising candidate for future observations. Despite its nondetection by ground-based detectors such as Advanced LIGO and Advanced Virgo, Callister et al. [Phys. Rev. X 7, 041058 (2017)] developed a Bayesian formalism to search for an isotropic SGWB with nontensorial polarizations, imposing constraints on signal amplitude in those components that violate general relativity using LIGO’s data. Since our ultimate aim is to estimate the spatial distribution of gravitational-wave sources, we have extended this existing method to allow for anisotropic components in signal models. We then examined the potential benefits from including these additional components. Using injection campaigns, we found that introducing anisotropic components into a signal model led to more significant identification of the signal itself and violations of general relativity. Moreover, the results of our Bayesian parameter estimation suggested that anisotropic components aid in breaking down degeneracies between different polarization components, allowing us to infer model parameters more precisely than through an isotropic analysis. In contrast, constraints on signal amplitude remained comparable in the absence of such a signal. Although these results might depend on the assumed source distribution on the sky, such as the Galactic plane, the formalism presented in this work has laid a foundation for establishing a generalized Bayesian analysis for an SGWB, including its anisotropies and nontensorial polarizations.

In the present work, we study four-dimensional black strings in Horndeski models with translation invariance. Imposing that the scalar field depends on the string-generator coordinate, the Klein-Gordon equation admits a linear profile as a solution. This relaxation allows finding rotating, asymptotically ${\mathrm{AdS}}_3\times \mathbb{R}$ black strings, dressed with an effective cosmological constant. In this regard, we show that in the full spectrum of shift-symmetric Horndeski theories with Einstein limit, the scalar charge needs to be fixed in terms of the parameter space. This method is employed to concrete examples to illustrate the scheme we go along with. Regarding the conserved charges, we compute them via the Euclidean method and show the fulfillment of the associated Smarr Law. Finally, we exhibit that our anti–de Sitter strings are locally and globally stable under small fluctuations around the equilibrium.

Gravitational waves (GWs) from binary neutron stars (NSs) have opened unique opportunities to constrain the nuclear equation of state by measuring tidal effects associated with the excitation of characteristic modes of the NSs. This includes gravitomagnetic modes induced by the Coriolis effect whose frequencies are proportional to the NS’s spin frequency. The NS’s spin orientation determines which subclass of gravitomagnetic modes are predominantly excited. We incorporate these effects in GW models needed for data analysis by encapsulating the adiabatic signatures from gravitomagnetic modes in slowly rotating NSs in an effective Love number which differs before and after a mode resonance and combining this with a known generic model for abrupt changes in the GWs at the mode resonance. This leads to an efficient approximate model that adds to a point-mass baseline and which we use to perform case studies of the impacts of gravitomagnetic effects for measurements with Cosmic Explorer, an envisioned next-generation GW detector. We quantify the extent to which neglecting (including) the effect of gravitomagnetic modes induces biases (significantly reduces statistical errors) in the measured tidal deformability parameters, which depend on the equation of state. Our results substantiate the importance of dynamical gravitomagnetic tidal effects for measurements with third-generation detectors.

We leverage recent breakthrough calculations using second-order gravitational self-force (2GSF) theory to improve both the gravitational-mode amplitudes and radiation-reaction force in effective-one-body (EOB) waveform models. We achieve this by introducing new calibration parameters in the SEOBNRv5HM mode amplitudes, and matching them to the newly available 2GSF energy-flux multipolar data for quasicircular nonspinning binary black holes. We find that this significantly improves the SEOBNRv5HM energy flux, when compared with numerical-relativity (NR) simulations of binary black holes with mass ratios between $1:1$ and $1:20$. Moreover, we find that, once the conservative part of the SEOBNRv5 dynamics is calibrated, the SEOBNRv5HM waveform model with 2GSF information reproduces the binding energy of NR simulations more accurately, providing a powerful check of the consistency and naturalness of the EOB approach. While we only include nonspinning 2GSF information, the more accurate binding energy and energy flux carry over to the SEOBNRv5 waveform models for spinning binary black holes. Thus, our results improve the latest generation of SEOBNR waveform models (i.e., SEOBNRv5), which has been recently completed for use in the upcoming fourth observing run (O4) of the LIGO-Virgo-KAGRA Collaboration.

Spin precession is one of the key physical effects that coul unveil the origin of the compact binaries detected by ground- and space-based gravitational-wave (GW) detectors, and shed light on their possible formation channels. Efficiently and accurately modeling the GW signals emitted by these systems is crucial to extract their properties. Here, we present SEOBNRv5PHM, a multipolar precessing-spin waveform model within the effective-one-body formalism for the full signal (i.e. inspiral, merger and ringdown) of binary black holes (BBHs). In the nonprecessing limit, the model reduces to SEOBNRv5HM, which is calibrated to 442 numerical-relativity (NR) simulations, 13 waveforms from BH perturbation theory, and nonspinning energy flux from second-order gravitational self-force theory. We remark that SEOBNRv5PHM is not calibrated to precessing-spin NR waveforms from the Simulating eXtreme Spacetimes Collaboration. We validate SEOBNRv5PHM by computing the unfaithfulness against 1543 precessing-spin NR waveforms, and find that for 99.8% (84.4%) of the cases, the maximum value, in the total mass range $20–300M_{\odot }$, is below 3% (1%). These numbers reduce to 95.3% (60.8%) when using the previous version of the SEOBNR family, SEOBNRv4PHM, and to 78.2% (38.3%) when using the state-of-the-art frequency-domain multipolar precessing-spin phenomenological IMRPhenomXPHM model. Due to much better computational efficiency of SEOBNRv5PHM compared to SEOBNRv4PHM, we are also able to perform extensive Bayesian parameter estimation on synthetic signals and GW events observed by LIGO-Virgo detectors. We show that SEOBNRv5PHM can be used as a standard tool for inference analyses to extract astrophysical and cosmological information of large catalogs of BBHs.

Waveform models are essential for gravitational-wave (GW) detection and parameter estimation of coalescing compact-object binaries. More accurate models are required for the increasing sensitivity of current and future GW detectors. The effective-one-body (EOB) formalism combines the post-Newtonian (PN) and small mass-ratio approximations with numerical-relativity results, and produces highly accurate inspiral-merger-ringdown waveforms. In this paper, we derive the analytical precessing-spin two-body dynamics for the SEOBNRv5 waveform model, which has been developed for the upcoming LIGO-Virgo-KAGRA observing run. We obtain an EOB Hamiltonian that reduces to the exact Kerr Hamiltonian in the test-mass limit. It includes the full 4PN precessing-spin information, and is valid for generic compact objects (i.e., for black holes or neutron stars). We also build an efficient and accurate EOB Hamiltonian that includes partial precessional effects, notably orbit-averaged in-plane spin effects for circular orbits, and derive 4PN-expanded precessing-spin equations of motion, consistent with such an EOB Hamiltonian. The results were used to build the computationally efficient precessing-spin multipolar SEOBNRv5PHM waveform model.

We present SEOBNRv5HM, a more accurate and faster inspiral-merger-ringdown gravitational waveform model for quasicircular, spinning, nonprecessing binary black holes within the effective-one-body (EOB) formalism. Compared to its predecessor, SEOBNRv4HM, the waveform model (i) incorporates recent high-order post-Newtonian results in the inspiral, with improved resummations, (ii) includes the gravitational modes $(\ell ,|m|)=(3,2),(4,3)$, in addition to the (2,2), (3,3), (2,1), (4,4), (5,5) modes already implemented in SEOBNRv4HM, (iii) is calibrated to larger mass ratios and spins using a catalog of 442 numerical-relativity (NR) simulations and 13 additional waveforms from black-hole perturbation theory, and (iv) incorporates information from second-order gravitational self-force in the nonspinning modes and radiation-reaction force. Computing the unfaithfulness against NR simulations, we find that for the dominant (2,2) mode the maximum unfaithfulness in the total mass range $10–300M_{\odot }$ is below ${10}^{-3}$ for 90% of the cases (38% for SEOBNRv4HM). When including all modes up to $\ell =5$ we find 98% (49%) of the cases with unfaithfulness below ${10}^{-2}$ (${10}^{-3}$), while these numbers reduce to 88% (5%) when using SEOBNRv4HM. Furthermore, the model shows improved agreement with NR in other dynamical quantities (e.g., the angular momentum flux and binding energy), providing a powerful check of its physical robustness. We implemented the waveform model in a high-performance python package (pyseobnr), which leads to evaluation times faster than SEOBNRv4HM by a factor of 10 to 50, depending on the configuration, and provides the flexibility to easily include spin-precession and eccentric effects, thus making it the starting point for a new generation of EOBNR waveform models (SEOBNRv5) to be employed for upcoming observing runs of the LIGO-Virgo-KAGRA detectors.

We numerically test quasiperiodic oscillations using three theoretically motivated models of spacetime, adopting neutron star sources. Then, we compare our findings with a spherically symmetric spacetime inferred from $F(R)$ gravity, with constant curvature, showing that it fully degenerates with our previous metrics that have been adopted in the context of general relativity. To do so, we work out eight neutron stars in low-mass x-ray binary systems and consider a Reissner-Nordström solution plus a de Sitter phase with unspecified sign for the cosmological constant term. In particular, we investigated three hierarchies, i.e., the first dealing with a genuine Schwarzschild spacetime, the second with de Sitter phase whose sign is not fixed a priori, and, finally, a Reissner-Nordström spacetime with an additional cosmological constant contribution. We perform Markov chain Monte Carlo analyses, based on the Metropolis-Hastings algorithm and infer $1\text{−}\sigma$ and $2\text{−}\sigma$ error bars. For all the sources, we find suitable agreement with spherical solutions with nonzero cosmological constant terms, i.e., with either de Sitter or anti–de Sitter solutions. From our findings, we notice that the existence of topological contribution to the net charge, suggested from $F(R)$ extensions of gravity, seems to be disfavored. Finally, we focus on the physics of the cosmological constant term here involved, investigating physical consequences and proposing possible extensions to improve our overall treatments.

We search for a stochastic gravitational wave background (SGWB) generated by a network of cosmic strings using six millisecond pulsars from Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian analysis considering two models for the network of cosmic string loops, and compare it to a simple power-law model which is expected from the population of supermassive black hole binaries. Our main strong assumption is that the previously reported common red noise process is a SGWB. We find that the one-parameter cosmic string model is slightly favored over a power-law model thanks to its simplicity. If we assume a two-component stochastic signal in the data (supermassive black hole binary population and the signal from cosmic strings), we get a 95% upper limit on the string tension of ${\log }_{10}(G\mu )<-9.9$ ($-10.5$) for the two cosmic string models we consider. In extended two-parameter string models, we were unable to constrain the number of kinks. We test two approximate and fast Bayesian data analysis methods against the most rigorous analysis and find consistent results. These two fast and efficient methods are applicable to all SGWBs, independent of their source, and will be crucial for analysis of extended datasets.

The next generation of ground-based gravitational-wave detectors, the Einstein Telescope and Cosmic Explorer, present a unique opportunity to put constraints on dense matter, among many other groundbreaking scientific goals. In a recent study, the science case of the Einstein Telescope was further strengthened, studying in particular the performances of different detector designs. In this paper we present a more detailed study of the nuclear physics section of that work. In particular, focusing on two different detector configurations (the single-site triangular-shaped design and a design consisting of two widely separated “L-shaped” interferometers), we study the detection prospects of binary neutron star (BNS) mergers, and how they can reshape our understanding of the underlying equation of state (EOS) of dense matter. We employ several state-of-the-art EOS models and state-of-the-art synthetic BNS merger catalogs, and we make use of the Fisher information formalism to quantify statistical errors on the astrophysical parameters describing individual BNS events. To check the reliability of the Fisher information formalism method, we further perform a full parameter estimation for a few simulated events. Based on the uncertainties on the tidal deformabilities associated to these events, we outline a mechanism to extract the underlying injected EOS using a recently developed metamodeling approach within a Bayesian framework. Our results suggest that with $\gtrsim 500$ events with signal-to-noise ratio greater than 12, we will be able to pin down very precisely the underlying EOS governing the neutron star matter.

We study the full phase diagram of a non-Hermitian $PT$-symmetric generalization of the paradigmatic two-dimensional massive Thirring model. Employing the nonperturbative functional renormalization group, we find that the model hosts a regime where $PT$ symmetry is spontaneously broken. This new phase is characterized by a relevant imaginary mass, corresponding to monstronic excitations displaying exponentially growing amplitudes for timelike intervals and tachyonic (Lieb-Robison-bound breaking, oscillatory) excitations for spacelike intervals. Furthermore, since the phase manifests itself as an unconventional attractive spinodal fixed point, which is typically unreachable in finite real-life systems, we find that the effective renormalized mass reached can be tuned through the microscopic parameters of the model. Our results further predict that the new phase is robust to external gauge fields, contrary to the celebrated BKT phase in the $PT$ unbroken sector. The gauge field then provides an effective and easy means to tune the renormalized imaginary mass through a wide range of values, and therefore the amplitude growth/oscillation rate of the corresponding excitations.

This work presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions at different rapidity scales, using lattice QCD. This is the first lattice QCD calculation of the kernel at quark masses corresponding to a close-to-physical value of the pion mass, with next-to-next-to-leading logarithmic matching to transverse-momentum-dependent parton distributions from the corresponding lattice-calculable distributions, and includes a complete analysis of systematic uncertainties arising from operator mixing. The kernel is extracted at transverse momentum scales $240\mathrm{MeV}\lesssim q_T\lesssim 1.6\mathrm{GeV}$ with a precision sufficient to begin to discriminate between different phenomenological models in the nonperturbative region.

We investigate the order of the QCD chiral transition in the limit of vanishing bare up/down quark masses and variations of the bare strange-quark mass $0\le m_{\mathrm{s}}\le \infty$. In this limit and due to universality long range correlations with the quantum numbers of pseudoscalar and scalar mesons may dominate the physics. In order to study the interplay between the microscopic quark and gluon degrees of freedom and the long range correlations we extend a combination of lattice Yang–Mills theory and a (truncated) version of Dyson-Schwinger equations by also taking backreactions of mesonic degrees of freedom into account. Both this system and the meson backcoupling approach have been studied extensively in the past but this is the first work in a full ($2+1$)-flavor setup. Starting from the physical point, we determine the chiral susceptibilities for decreasing up/down quark masses and find good agreement with both lattice and functional renormalization group results. We then proceed to determine the order of the chiral transition along the left-hand side of the Columbia plot, for chemical potentials in the range $-(30\mathrm{MeV}{)}^2\le {\mu }_q^2\le (30\mathrm{MeV}{)}^2$. We find a second-order phase transition throughout and no trace of a first-order region in the $N_f=3$ corner of the Columbia plot. This result remains unchanged when an additional Goldstone boson due to a restored axial ${\mathrm{U}}_A(1)$ is taken into account.

We search for the tree-diagram dominated process $B^{+}\to p\overline{n}{\pi }^0$, using a data sample of $772\times {10}^{6}B\overline{B}$ pairs collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. This is the first search with the Belle detector for a decay mode including an antineutron. No significant signal is observed and a 90% credible upper limit on the branching fraction is set at $6.3\times {10}^{-6}$.

According to Bekenstein’s area law, the black hole entropy is identified holographically with one quarter of the horizon area. However, it is commonly believed that such a law is only valid in Einstein’s theory and that higher curvature corrections generically give rise to its modifications. This is, for example, the case of black holes in Lovelock gravities, or their four-dimensional cousins in the recently discovered 4D scalar-tensor Gauss-Bonnet gravity where one naively “finds” (classical) logarithmic corrections to the Bekenstein’s law. In this paper we argue that such logarithmic corrections originate from ignoring the shift symmetry of the 4D Gauss-Bonnet gravity. When this symmetry is properly taken into account, there is no longer any departure from the area law in this theory. Moreover, the first law remains valid upon modifying the black hole temperature, which can be derived via the Euclidean grand canonical ensemble (Brown-York) procedure, but is no longer given by the surface gravity. Interestingly, we show that upon similar modification of the black hole temperature the area law can also prevail for black holes in higher-dimensional Lovelock gravities.

The identification and isolation of two weakly interacting massive particles (WIMP) dark matter (DM) components at colliders is of wide interest on the one hand but extremely challenging on the other, especially when the dominant signal of both DM components is of the mono-$X$ type ($X=\gamma$, $Z$, $H$). After emphasizing that an $e^{+}{e}^{-}$ collider is more suitable for this goal, we first identify the theoretical principles that govern the occurrence of two peaks in missing energy ($\cancel{E}$) distribution, in a double-DM scenario. We then identify a variable that rather spectacularly elicits the double-peaking behavior, namely, the plot of bin-wise statistical significance ($S/\sqrt{B}$) against $\cancel{E}$. Using Gaussian fits of the histograms, we apply a set of criteria developed by us, to illustrate the above points numerically for suitable benchmarks.

We prove that the tree-level scattering amplitudes for (super) Yang-Mills theory in arbitrary dimensions and for M2-brane models exhibit color-kinematics (CK) duality. Our proof for Yang-Mills theory substantially simplifies existing ones in that it relies on the action alone and does not involve any computation; the proof for M2-brane models establishes this result for the first time. Explicitly, we combine the facts that Chern-Simons-type theories naturally come with a kinematic Lie algebra and that both Yang-Mills theory and M2-brane models are of Chern-Simons form when formulated in pure spinor space, extending previous work on Yang-Mills currents [M. Ben-Shahar and M. Guillen, J. High Energy Phys. 12 (2021) 014]. Our formulation also provides explicit kinematic Lie algebras for the theories under consideration in the form of diffeomorphisms on pure spinor space. The pure spinor formulation of CK-duality is based on ordinary, cubic vertices, but we explain how ordinary CK-duality relates to notions of quartic-vertex 3-Lie algebra CK-duality for M2-brane models previously discussed in the literature.

The closed-form solution of the 1.5 post-Newtonian (PN) accurate binary black hole (BBH) Hamiltonian system has proven to be evasive for a long time since the introduction of the system in 1966. Solutions of the PN BBH systems with arbitrary parameters (masses, spins, eccentricity) are required for modeling the gravitational waves emitted by them. Accurate models of gravitational waves are crucial for their detection by LIGO/Virgo and LISA. Only recently, two solution methods for solving the BBH dynamics were proposed in Ref. [G. Cho and H. M. Lee, Phys. Rev. D 100, 044046 (2019)] (without using action-angle variables), and Refs. [S. Tanay et al., Phys. Rev. D 103, 064066 (2021), S. Tanay et al., Phys. Rev. D 107, 103040 (2023)] (action-angle based). This paper combines the ideas laid out in the above articles, fills the missing gaps and compiles the two solutions which are fully 1.5PN accurate. We also present a public Mathematica package bbhpntoolkit which implements these two solutions and compares them with the result of numerical integration of the evolution equations. The level of agreement between these solutions provides a numerical verification for all the five action variables constructed in Refs. [S. Tanay et al., Phys. Rev. D 103, 064066 (2021), S. Tanay et al., Phys. Rev. D 107, 103040 (2023)]. This paper hence serves as a stepping stone for pushing the action-angle-based solution to 2PN order via canonical perturbation theory.