In this paper, we have studied the general generating function of reduction for one-loop integrals with arbitrary tensor structure in the numerator and arbitrary power distribution of propagators in the denominator. Using integration-by-part relations, we have established the partial differential equations for these generating functions and solved them analytically with compact form. These results provide useful information for the analytical structure of reduction coefficients and guidance for applying the generating function method to reductions of higher loop integrals.

We present a comparison of different quantum state preparation algorithms and their overall efficiency for the Schwinger model with a theta term. While adiabatic state preparation is proved to be effective, in practice it leads to large cnot gate counts to prepare the ground state. The quantum approximate optimization algorithm (QAOA) provides excellent results while keeping the cnot counts small by design, at the cost of an expensive classical minimization process. We introduce a “blocked” modification of the Schwinger Hamiltonian to be used in the QAOA that further decreases the length of the algorithms as the size of the problem is increased. The rodeo algorithm (RA) provides a powerful tool to efficiently prepare any eigenstate of the Hamiltonian, as long as its overlap with the initial guess is large enough. We obtain the best results when combining the blocked QAOA ansatz and the RA, as this provides an excellent initial state with a relatively short algorithm without the need to perform any classical steps for large problem sizes.

In this paper, we discuss a novel method to search for inhomogeneous chiral symmetry breaking in theories with fermions. The prime application we have in mind is QCD, but the method is also applicable for other theories, including solid state applications. It is based on an extension of the chiral susceptibility to inhomogeneous phases, and it works as a stability analysis. Our method allows us to determine when homogeneous solutions have the tendency to create spatially modulated condensates. As proof of principle, we apply this technique to a rainbow-ladder QCD model and find that its phase diagram contains an inhomogeneous region.

Homogeneity is the hallmark of standard candle-based cosmology investigations. Thermonuclear supernovae (Type-Ia, SNeIa) violate this essential requirement if they develop along multiple evolutionary pathways. In this work, the impact of thermonuclear diversity on cosmological parameter constraints is quantified using Pantheon+, one of the largest ensembles of SNeIa compiled to probe cosmology to date. Evidence of diversity is encoded in supernova light curves. Pantheon+ is shown to be diverse, with features indicative of multiple thermonuclear subclasses. Diversity driven systematic effects have been quantified on a supernova-by-supernova basis; event selections based on light curve derived metrics were subsequently used to characterize diversity dependent trends and limit their impact. A diversity mitigated estimate of the Hubble-Lemaître parameter, $H_0=67.9\pm 0.8\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ (68% C.L.), was obtained by reanalyzing Pantheon+. The Hubble tension, an apparent disparity between early and late Universe determinations of $H_0$, is eased from $\sim 5\sigma$ to $<1\sigma$ after accounting for the diverse thermonuclear scenarios that govern SNeIa. Diversity mitigated subsets of Pantheon+ also show a $\sim 3.4\sigma$ preference for a flat $w_0{w}_a\mathrm{CDM}$ cosmology with dark energy equation of state parameters $(w_0,w_a)=(-1.084\pm 0.180,-2.066\pm 0.675)$. A strategy for precise SNeIa-derived cosmological inferences, dominated by statistical rather than systematic uncertainties, is also presented.

Analyzing the supersymmetric Pati-Salam landscape on a ${\mathbb{T}}^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ orientifold in IIA string theory, we have found only two models that accurately account for all standard model fermion masses and mixings. The models are dual to each other under the exchange of two SU(2) sectors and feature 12 adjoint scalars, the maximum number allowed in the landscape, whose linear combination yields the two light Higgs eigenstates. Dirac neutrino masses in normal ordering of $(50.6,10.6,6.2)\pm 0.1\mathrm{meV}$ satisfy both the experimental as well as swampland constraints.

General relativity predicts the presence of a singularity inside of a black hole revealing that it is not a complete theory of gravity. A real structure of a black hole interior near an expected singularity depends on the UV completion of gravity. In this paper we address the question of whether singular spherically symmetric solutions are absent (or present) in a complete gravity theory. We find that the answer is governed by the functional form of a nonperturbative graviton propagator. A ghost-free infinite derivative gravity is favored by the unitarity the graviton propagator of an exponential form. We explicitly show in this framework that a singularity is not possible unless an unphysical situation when a mass of the black hole is infinite is considered.

In recent years, the effects of removing infinitesimal Gribov copies from the path integral of gauge-fixed Yang-Mills-Chern-Simons theories formulated in three-dimensional Euclidean space have been investigated. Part of the interest resides in the fact that such an elimination of gauge copies introduces a mass parameter, the Gribov parameter, which is relevant when the assumptions of the Faddeev-Popov procedure are not well grounded. Such a parameter enters the propagator of the gauge field, which is topologically massive due to the Chern-Simons term. The resulting action, which eliminates infinitesimal Gribov copies in this context, has been constructed in linear covariant gauges, and the interplay between the aforementioned mass parameters allows for a rich phase diagram in which confining and deconfining signatures are observed in the gauge-field propagator. In the present work, we establish the renormalization properties of such a theory at all orders in perturbation theory by means of the algebraic renormalization framework and show that the removal of infinitesimal Gribov copies does not affect the standard nonrenormalization properties of standard gauge-fixed Yang-Mills-Chern-Simons theories, i.e., the theory is finite.

The real-time propagator of the symmetric Rosen-Morse, also known as the symmetric modified Pöschl-Teller, barrier is expressed in the Picard-Lefschetz path integral formalism using real and complex classical paths. We explain how the interference pattern in the real-time propagator and energy propagator is organized by caustics and Stokes phenomena and list the relevant real and complex classical paths as a function of the initial and final position. We discover the occurrence of singularity crossings, where the analytic continuation of the complex classical path no longer satisfies the boundary value problem and needs to be analytically continued. Moreover, we demonstrate how these singularity crossings play a central role in the real-time description of quantum tunneling.

Potentials arising in ultraviolet-completed field theories can be devoid of singularities, and hence render spacetimes simply connected. This challenges the notion of topological invariants considered in such scenarios. We explore the classical implications for (i) electrodynamics in flat spacetime, (ii) ultrarelativistic gyratonic solutions of weak-field gravity, and (iii) the Reissner-Nordström black hole in general relativity. In linear theories, regularity spoils the character of topological invariants and leads to radius-dependent Aharonov-Bohm phases, which are potentially observable for large winding numbers. In general relativity, the physics is richer: The electromagnetic field can be regular and maintain its usual topological invariants, and the resulting geometry can be interpreted as a Reissner-Nordström black hole with a spacetime region of coordinate radius $\sim q^2/(GM)$ cut out. This guarantees the regularity of linear and quadratic curvature invariants ($\mathcal{R}$ and ${\mathcal{R}}^2$), but does not resolve singularities in invariants such as ${\mathcal{R}}^p{\square }^n{\mathcal{R}}^q$, reflected by conical or solid angle defects. This motivates that gravitational models beyond general relativity need to be considered. These connections between regularity (= UV properties of field theories) and topological invariants (= IR observables) may hence present an intriguing avenue to search for traces of new physics and identify promising modified gravity theories.

In this paper, we investigate the gravitational lensing and accretion disk imaging characteristics of a dense core modeled by the Buchdahl spacetime. By imposing the appropriate energy conditions and ensuring the absence of curvature singularities, we delineate the parameter space in which the dense core mimics key gravitational features of black holes while exhibiting unique deviations. We derive the photon orbital equation and calculate deflection angles, clearly distinguishing between weak- and strong-deflection regimes. Furthermore, we construct a mapping from the illuminated, geometrically thin accretion disk onto the observer’s screen—focusing on the isoradial curves corresponding to a representative source ring. For compactness values below a critical threshold, only a finite number of disk images are formed. In this range, their secondary and higher-order images typically display double-loop structures, with each loop individually capturing the entire source ring. Notably, the highest-order image sometimes appears as a single, crescent-shaped loop that does not enclose the screen’s center, implying the existence of a cutoff angle that restricts the imaged portion of the source ring. In contrast, for compactness values above the critical threshold, an infinite sequence of double-loop structures appears—a behavior closely linked to the presence of a photon sphere. These findings suggest that the lensing signatures of dense cores can distinguish them from black holes, offering new insights for high-resolution observations.

Inspired by the so-called Palatini formulation of general relativity and of its modifications and extensions, we consider an analogous formulation of the dynamics of a self-interacting gauge field which is determined by nonlinear extension of Maxwell’s theory, usually known as nonlinear electrodynamics. In this first order formalism the field strength and the gauge potential are treated, a priori as independent, and, as such, varied independently in order to produce the field equations. Accordingly we consider within this formalism alternative and generalized nonlinear Lagrangian densities, some of them of a new kind which gives up the restriction of equivalence to second order Lagrangians. Several new spherically symmetric objects are constructed analytically and their main properties are studied. The solutions are obtained in flat spacetime ignoring gravity and for the self-gravitating case with emphasis on black holes. As a background for comparison between the first and second order formalisms, some of the solutions are obtained by the conventional second order formalism, while for others a first order formalism is applied. Among the self-gravitating solutions we find new families of black holes and study their main characteristics. Some of the flat space solutions can regularize the total energy of a point charge and a subset of them exhibit also finite field strength and energy density, although their black hole counterparts are not regular.

In this work, we examine the entanglement dynamics of two massive particles confined within their respective infinite square potential wells induced by gravity. Assuming that each particle is initially in the ground state of its infinite square well, we investigate the formation of entanglement between the particles as a result of their gravitational interaction during their adiabatic movement toward each other. Our results reveal that, under suitable parameters, entanglement swiftly emerges. Compared to previous schemes, our approach significantly reduces the particle mass, greatly lowering the experimental threshold.

Simulation of quasicircular compact binaries is a major goal in numerical relativity, as they are expected to constitute most gravitational wave observations. However, given that orbital eccentricity is not well defined in general relativity, providing initial data for such binaries is a challenge for numerical simulations. Most numerical relativity codes obtain initial conditions for low-eccentricity binary simulations by iterating over a sequence of short simulations—measuring eccentricity mid-evolution and correcting the initial data parameters accordingly. Eccentricity measurement depends on a numerically challenging nonlinear fit to an estimator model, and the resulting eccentricity estimate is extremely sensitive to small changes in how the fit is performed. We have developed an improved algorithm that produces more consistent measurements of eccentricity relative to the time window chosen for fitting. The primary innovations are the use of the nonlinear optimization algorithm, variable projection, in place of more conventional routines, an initial fit parameter guess taken from the trajectory frequency spectrum, and additional frequency processing of the trajectory data prior to fitting.

Gravitational lensing of gravitational waves provides us with much information about the Universe, including the dark matter distribution at small scales. The information about lensed gravitational waves is encapsulated by an amplification factor, which is calculated by an integration of an oscillatory function. The Born approximation, which has been studied in terms of wave optics in gravitational lensing, may provide a means of overcoming the difficulty in evaluating the oscillating function and better understanding the connection between the amplification factor and the lens mass distribution. In this paper, we revisit the Born approximation for a single lens plane. We find that the distortion of gravitational waves induced by wave optics gravitational lensing is in general connected with the mass distribution of the lens object through a convolution integral, where the scale of the kernel is determined by the Fresnel scale. We then study the validity and accuracy of the Born approximation specifically for the case of a point mass lens for which the exact analytical expression of the amplification factor is available. Using the dimensionless parameter $y$, which represents the normalized impact parameter, and the dimensionless parameter $w$, which denotes the normalized frequency, we show that the $n$th term of the Born approximation scales as $y^{-2}{w}^{n-1}$. This indicates that, for the case of a point mass lens, the Born approximation is valid when $w$ is less than 1, with its accuracy scaling as $w{y}^{-2}$ in this regime.

Pulsar timing array (PTA) observations have recently gathered substantial evidence for the existence of a gravitational wave background in the nHz frequency band. Searching for anisotropies in this signal is key to determining its origin and in particular to distinguish possible astrophysical from cosmological sources. In this work, we assess the sensitivity of current and future pulsar timing arrays to such anisotropies using the full covariance matrix of pulsar timing delays. While current day pulsar timing arrays can only set mildly informative constraints on the dipole and quadrupole, we show that percent-level accuracy for several low multipoles can be achieved in the near future. Moreover, we demonstrate that anisotropies in the gravitational wave background and the Hellings-Downs angular correlation, indicating the presence of gravitational waves, are approximately uncorrelated and can hence be reconstructed independently. These results can be reproduced with fastpta, a publicly available python code to forecast the constraining power of PTA configurations.

We investigate the influence of dark matter on hybrid stars. Using a two-fluid approach, where normal and dark matter components interact only gravitationally, we explore how dark matter can trigger the appearance of quark matter in neutron stars for unprecedented low masses. Our findings reveal that dark matter increases the central pressure of neutron stars, potentially leading to the formation of hybrid stars with quark cores even at very low compact star masses. The critical mass for the appearance of quark matter decreases with increasing dark matter content. We introduce the concept of “masquerading hybrid stars,” where dark matter admixed stars exhibit similar mass-radius relations to purely hadronic stars, making it challenging to distinguish between them based solely on these parameters. Additionally, we identify a unique class of objects termed “dark oysters,” characterized by a large dark matter halo and a small normal matter core, highlighting the diverse structural possibilities for compact stars influenced by dark matter.

A number of new balloon or space-based $\gamma$-ray observatories have been proposed to close a “MeV gap” in sensitivity to $\gamma$ rays in the MeV–GeV energy band. One aspect of the science case for these instruments is their ability to constrain or discover decaying or annihilating dark matter. In this work, we forecast the sensitivity of these instruments for dark matter annihilation or decay for a range of possible Standard Model final states and compare to existing bounds.

We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to obtain a series expansion of this system’s far-from-equilibrium attractor. This expansion possesses a finite radius of convergence, which proves the existence of the attractor. Furthermore, the series can be analytically continued to late times and we find that this procedure reproduces the known values of shear viscosity and other transport coefficients to high accuracy. We also provide a simple approximate analytic expression that describes the attractor in the entire domain of interest for studies of quark-gluon plasma dynamics.

We present the results obtained by performing global fits of two-Higgs-doublet models (2HDMs) using the full Run 1 and Run 2 Higgs datasets collected at the LHC. Avoiding unwanted tree-level flavor-changing neutral currents and including the wrong-sign cases, we consider 12 scenarios across six types of 2HDMs: Inert, type I, type II, type III, type IV, and aligned 2HDMs. Our main results are presented in Table III and Fig. 1. We find that the type-I 2HDM provides the best fit, while the wrong-sign scenarios of the type-II and type-IV 2HDMs, where the normalized Yukawa coupling to down-type quarks is opposite in sign to the Standard Model (SM), are disfavored. We also observe that the aligned 2HDM gives the second-best fit when the Yukawa couplings to down-type quarks take the same sign as in the SM, regardless of the sign of the Yukawa couplings to the charged leptons.