Renormalization-group equations (RGE) is one of the key tools in studying high-energy behavior of the Standard Model (SM). We begin by reviewing one-loop RGE for the dimensionless couplings of the SM and proceed to the state-of-the-art results. Our study focuses on the RGE solutions at different loop orders. We compare not only the standard (“diagonal”) loop counting when one considers gauge, Yukawa, and scalar self-coupling beta functions at the same order but also “nondiagonal” ones, inspired by the so-called Weyl consistency conditions. We discuss the initial conditions for RGE (“matching”) for different loop configurations and study the uncertainties of running couplings both related to the limited precision of the experimental input (“parametric”) and the missing high-order corrections (“theoretical”). As an application of our analysis we also estimate the electroweak vacuum decay probability and study how the uncertainties in the running parameters affect the latter. We argue that nondiagonal beta functions, if coupled with a more consistent nondiagonal matching, lead to larger theoretical uncertainty than diagonal ones.

We show that the gravitational Green-Schwarz (GS) transformation becomes trivial in the nonrelativistic (NR) limit of ten-dimensional heterotic supergravity with four-derivative corrections. This constitutes an important step towards establishing the trivialization of the GS mechanism in this limit. In this work, we perform a NR expansion of the Kalb-Ramond field and identify the finite Green-Schwarz transformation in this limit, which can be interpreted as a noncovariant $SO(8)$ transformation. We then construct an explicit field redefinition such that the redefined two-form is invariant under this symmetry. This result is compared with the previously reported trivialization of the gauge GS mechanism under the same limit. Both field redefinitions can be implemented simultaneously, and the associated Chern-Simons terms are exact, arising directly from the redefinition structure, and leading to a trivial Bianchi identity. These results support the expectation that anomaly cancellation becomes automatic in the NR regime, and therefore we discuss their potential implications.

The five-dimensional loop quantum Kaluza-Klein cosmology is constructed based on the symmetric reduction of the connection formulation of the full theory. Through semiclassical analysis, the effective scalar constraint for the cosmological model coupled with a dust field is derived, incorporating the quantum fluctuations of geometry as a subleading-order correction. It demonstrates that the quantum model has the correct classical limit. The explicit solutions to the equations of motion show that the big bang and past big rip singularities in the classical model are avoided by a quantum bounce and a quantum collapse respectively in the effective model. In a particular scenario, the dynamical compactification of the extra dimension is realized, while the observable four-dimensional universe transitions through three distinct epochs: (i) A superinflationary phase generating 55 e-folds; (ii) A decelerated expansion era; (iii) A late-time accelerated expansion phase driven by quantum fluctuations. These results suggest that both cosmic inflation and dark energy may originate from the interplay between the compact extra dimension and quantum geometric effects.

We present a novel framework for analyzing four-body semileptonic weak decays, performing the first high-twist analysis of the $D_s\to {[\pi \pi ]}_{\mathrm{S}}$ form factors using light cone distribution amplitudes for the isoscalar two-pion state ($2\pi \mathrm{DAs}$). It is motivated by persistent tensions between phenomenological cascade analyses and QCD-based interpretations of the partonic structure of the $f_0$ meson. Our study reveals that the twist-three $2\pi$ DAs incorporate an asymmetry in the partial-wave expansion, a feature absent in single $f_0$ distribution amplitudes, that drives a substantial cancellation between twist-two and twist-three contributions to the form factors. As a result, the predicted decay rate falls significantly below the experimental value. These findings indicate that the isoscalar two-pion system near the charm scale is not primarily a $q\overline{q}$ state, reviving the energy-dependent partonic structures of light scalar mesons by highlighting a fundamental limitation of the single-meson light cone distribution amplitude approach in describing such complex systems.

In high-energy physics, confinement denotes the tendency of fundamental particles to remain bound together, preventing their observation as free, isolated entities. Interestingly, analogous confinement behavior emerges in certain condensed matter systems, for instance, in the Ising model with both transverse and longitudinal fields, where domain walls become confined into meson-like bound states as a result of a longitudinal field-induced linear potential. In this work, we employ the Ising model to demonstrate that Krylov state complexity—a measure quantifying the spread of quantum information under the repeated action of the Hamiltonian on a quantum state—serves as a sensitive and quantitative probe of confinement. We show that confinement manifests as a pronounced suppression of Krylov complexity growth following quenches within the ferromagnetic phase in the presence of a longitudinal field, reflecting slow correlation dynamics. In contrast, while quenches within the paramagnetic phase exhibit enhanced complexity with increasing longitudinal field, reflecting the absence of confinement, those crossing the critical point to the ferromagnetic phase reveal a distinct regime characterized by orders-of-magnitude larger complexity and display trends of weak confinement. Notably, in the confining regime, the complexity oscillates at frequencies corresponding to the meson masses, with its power-spectrum peaks closely matching the semiclassical predictions.

In this paper, we study excited states in anti–de Sitter (AdS) space prepared by local operator insertions of a massive scalar field, corresponding to local operator quenches in a free bulk scalar theory. Using the AdS/CFT correspondence, we compute the time evolution of boundary observables in the dual conformal field theory states. We then introduce a hard wall in AdS Poincare coordinates to impose an infrared cutoff (“hard wall”), thereby creating a confining deformation of the dual conformal field theory, and analyze the dynamics of excited states in this confining background. By comparing the evolution of boundary two-point correlation functions in the deformed theory with the statistics of Gaussian random matrix ensembles, we show that for sufficiently heavy operators, the spacing-ratio statistics of peaks in the temporal dynamics are closest to those of the Gaussian symplectic ensemble. Finally, we extend the analysis to the compact Bañados-Teitelboim-Zanelli black hole and to its hard-wall deformation, where we find qualitatively similar trends.

In this article, we show that several self-dual spacetimes previously studied in the context of celestial and twisted holography arise as limits of a certain Taub-NUT ${\mathrm{AdS}}_4$ metric, the Pedersen metric, in which their mass, NUT charge, and cosmological constant obey a self-duality relation. In particular, self-dual Taub-NUT, a singular double cover of Eguchi-Hanson space, Euclidean ${\mathrm{AdS}}_4$, and noncompact ${\mathbb{C}\mathbb{P}}^2$, which is conformally equivalent to Burns space, arise as special limits of the Pedersen metric. The Pedersen metric can be derived from a curved twistor space which we conjecture to arise from a backreaction of self-dual gravity in the presence of a cosmological constant when coupled to a defect operator wrapping a certain ${\mathbb{C}\mathbb{P}}^1$ at infinity. The curved twistor space gives rise to a 2-parameter deformation of the celestial symmetry algebra $L{w}_{\wedge }$ which reduces to previously studied algebras in various limits.

We propose a novel nonlocal spin-$1/2$ theory in which the form factor depends on the Dirac operator rather than on the d’Alembert operator. In this scenario, we explore some classical and quantum aspects of this new theory. At the classical level, we investigate the dispersion relation of free spin-$1/2$ particles and find that it increasingly deviates from the standard case as the nonlocal effects become relevant. At the quantum level, we compute the fermionic one-loop effective action for the nonlocal spin-$1/2$ theory with Yukawa coupling and show that the contributions of nonlocal effects are significant in the UV limit, while in the IR they are suppressed by a UV cutoff scale, which has been chosen to coincide with the nonlocality scale $\mathrm{\Lambda }$. We minimally couple a $U(1)$ gauge field to the nonlocal spin-$1/2$ field theory and explicitly demonstrate that this theory is gauge invariant. Finally, we obtain a nonlocal version of the Pauli equation and the impact of the nonlocality in the $g$-factor of massive particles.

For the solitons of the theory including topological terms, the standard collective coordinate quantization does not construct the proper low energy effective theory. In the presence of topological terms, zero modes are classified into three groups: dynamical zero modes with constant velocity, cyclotron zero modes in a circular orbit, and static constraint zero modes. According to the mode expansion, the topological term contributes to the moduli metric of the dynamical zero modes. In addition, constraint zero modes do not have the kinetic term and produce constraints that strongly restrict the spectrum instead. In this paper, we propose a generalized collective coordinate quantization method and apply it to the $SU(3)$ Skyrmion with the Wess-Zumino-Witten term. We find five constraints. These reproduce the results of Cherman et al. [The collective quantization of three-flavored skyrmions revisited, Phys. Rev. D 72, 094015 (2005)], eliminating all the $SU(3)$ multiplets except the nucleon octet and $\mathrm{\Delta }$ baryon decuplet from the collective coordinate part of the spectrum.

Gravitational waves from spin-precessing binaries exhibit equatorial asymmetries absent in nonprecessing systems, leading to net linear momentum emission and contributing to the remnant’s recoil. This effect, recently incorporated into only a few waveform models, is crucial for accurate recoil predictions and improved parameter estimation. We present an upgrade to the seobnrv5phm model—${\mathrm{SEOBNRv}5\mathrm{PHM}}_{\mathrm{w}/\mathrm{asym}}$—which includes equatorial asymmetric contributions to the $\ell =m\le 4$ waveform modes in the co-precessing frame. The model combines post-Newtonian inputs with calibrated amplitude and phase corrections and a phenomenological merger-ringdown description, tuned against 1523 quasicircular spin-precessing numerical relativity waveforms and single-spin-precessing test-body plunging-geodesic waveforms. We find that ${\mathrm{SEOBNRv}5\mathrm{PHM}}_{\mathrm{w}/\mathrm{asym}}$ improves the agreement with numerical relativity waveforms across inclinations, with median unfaithfulness reduced by up to 50% compared to seobnrv5phm, and achieves 30%–60% lower unfaithfulness than imrphenomxpnr and 76%–80% lower than teobresums_dali. The model significantly improves the prediction of the recoil velocity, reducing the median relative error with numerical relativity from 70% to 1%. Bayesian inference on synthetic injections demonstrates improved recovery of spin orientations and mass parameters, and a reanalysis of GW200129 shows a threefold increase in the spin-precessing Bayes factor, highlighting the importance of these effects for interpreting spin-precessing events.

We investigate the impact of shot noise on the stochastic gravitational wave background generated by binary neutron star mergers, and confirm that the overall background can be significantly influenced by relatively few neighboring, loud events. To mitigate the shot noise, we propose a procedure to remove nearby events by notching them out in the time-frequency domain. Additionally, we quantify the cosmic/sample variance of the resulting background after notching, and we study the deviation between the cross-correlation measurement and the theoretical prediction of the background. Taking both effects into account, we find that the resulting sensitivity loss in the search for an isotropic background formed by binary neutron star mergers is minimal, and is limited to $\lesssim 4\%$ below 40 Hz, and to $\lesssim 1\%$ above 40 Hz.

The background subtraction method has long served as a practical tool for computing the Euclidean action and thermodynamic quantities of black holes. While its equivalence to the Iyer-Wald formalism is well understood in pure gravity theories, its validity in matter-coupled theories remains less clear and has even been questioned in the literature. In this work, we revisit this issue and demonstrate that the equivalence between the Euclidean action method and the Iyer-Wald formalism persists in matter-coupled scenarios. We apply the resulting formulation to two representative examples of such theories, and in both cases, the Euclidean approach performs smoothly. We further identify situations where the method may encounter subtleties due to the special properties of certain matter fields. Our results clarify when background subtraction remains reliable beyond pure gravity and when additional care is necessary.

We propose a method for separating and detecting the nontensor modes of stochastic gravitational-wave backgrounds (SGWBs) using networks of space-based gravitational-wave detectors. We consider four distinct data-reconstruction schemes for the coinclination and anti-inclination orbital configurations of the LISA-Taiji network. We find that the coinclination configuration offers its advantages over the anti-inclination one and can achieve signal-to-noise ratios up to 17.3 for the vector modes and 10.4 for the scalar modes with the energy density spectrum as ${\mathrm{\Omega }}_{\mathrm{GW}}^p(f)={10}^{-12}$. Our method can be used to measure beyond-general-relativity polarization modes of SGWBs at the mHz frequency band, opening a new avenue for testing alternative gravity theories.

Binary neutron star mergers provide a laboratory for probing fundamental physics through their gravitational-wave emission and electromagnetic counterparts. In particular, they may allow us to explore signatures of physics beyond the Standard Model in strong-gravity regimes, such as those of dark matter. In this work, we investigate the dynamics of light dark matter, modeled as a minimally coupled scalar field, surrounding a binary neutron star system. Our primary focus is to assess whether the scalar field remains bound to the binary over the late inspiral-merger timescales and to determine its potential impact on observable signatures. We find that, in a range of scenarios, the scalar field forms a common cloud around the binary that does not disperse. At sufficiently high densities, this leads to measurable effects, including a dephasing of the binary inspiral, a less compact postmerger remnant, and suppression of the dynamical ejecta. For densities motivated by astrophysical considerations, however, these effects remain small and are unlikely to be detectable with current or next-generation gravitational-wave observatories.

Ultralight axions (ULAs) are hypothetical particles which can behave like dark matter (DM) or dark energy (DE) depending on masses generated at the symmetry-breaking scale. It remains a mystery whether the ULAs can make up a fraction of DM or DE. Although theoretical predictions indicate that the ULAs may leave distinct imprints on cosmological signals, these signatures may exist in a broad spatial and temporal scales, and may be degenerate with the known effects of the standard model. The ULA signatures are extremely subtle and the observational evidence of the ULAs remain elusive. In this work, we infer the ULA properties using both the early and late universe observations from the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO). We validate modeling of the ULA effects using the CMB and BAO mock data and perform different tests to cross-check the results. By analyzing the Planck 2018 CMB measurements and the BAO measurements from the Data Release 2 of Dark Energy Spectroscopic Instrument (DESI), we constrain the energy density fraction ratio of the ULAs to total dark matter ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_d$ and obtain a new upper bound of ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_d$. Future CMB and BAO measurements will achieve unprecedented precision and will be crucial for understanding the nature of the ULAs.

We develop a highly accurate analytic approximation for small-scale noncold relic perturbations by solving the collisionless Boltzmann equation in the quasistationary regime. The approximation is implemented in CLASSIER (CLASS Integral Equation Revision), a modified version of the Boltzmann solver CLASS that replaces the traditional truncated Boltzmann hierarchy of noncold relic multipoles with a small set of integral equations solved iteratively. Applying it to massive neutrinos yields a factor-of-two reduction in total run-time relative to CLASSIER without the approximation. Compared to standard CLASS runs (with ${\ell }_{\max }^{\mathrm{NCDM}}=40$ and no late-time massive neutrino fluid approximation) under the same precision setting, CLASSIER with this approximation is faster by a factor of 3–6. The approximation faithfully reproduces the late-time behavior of massive neutrino perturbations and preserves sub-0.1% accuracy in the matter power spectrum today up to comoving wave number $k=100{\mathrm{Mpc}}^{-1}$. With this approximation, massive-neutrino perturbations are no longer the computational bottleneck on small scales for linear-theory predictions. The approach can be readily extendable to nonstandard dark-matter models and offers prospects for further efficiency gains in high-precision cosmological analyses.

We investigate the impact of a nonminimal coupling between curvature and inflaton field within the spontaneous baryogenesis background. We demonstrate that this coupling leads to a significant enhancement in particle production, even for small values of the coupling constant $\xi$. Assuming a perfectly homogeneous and isotropic universe during the reheating phase, we study the inflaton decay into fermion-antifermion pairs by means of a semiclassical approach, treating fermions as quantized fields and considering the inflaton and the Ricci scalar as classical quantities. We adopt the simplest approach in which the inflaton is minimally coupled to baryons and nonminimally with gravity. In particular, we solve the equations of motion for the inflaton to first order in perturbation theory, with $\xi$ serving as perturbative parameter. Afterward, we compute the difference in the number densities of baryons and antibaryons produced through the inflaton decay into fermion-antifermion pairs. We show that the nonminimal coupling term de facto increases inflaton mass for negative values of $\xi$, letting fermion-antifermion decays be more probable and thus enhancing the overall baryogenesis process. Quite the opposite, the baryon asymmetry is reduced for positive values of the coupling constant. Finally, since the fermionic fields appear not to be mass eigenstates, we specialize the mass mixing between them only. To this end, we thus include the effects of mass- mixing and cosmic expansion into our calculations. Physical consequences of baryon production are therefore explored.

We performed computational gravitational backreaction on cosmic string loops taken from a network simulation. The principal effect of backreaction is to smooth out small-scale structure on loops, which we demonstrate by various measures including the average loop power spectrum and the distribution of kink angles on the loops. Backreaction does lead to self-intersections in most cases, but these are typically small. An important effect discussed in prior work is the rounding off of kinks to form cusps, but we find that the cusps produced by that process are very weak and do not significantly contribute to the total gravitational-wave radiation of the loop. We comment briefly on extrapolating our results to loops as they would be found in nature.