We study the phase structure of the ($3+1$)-dimensional cold and dense QCD with the Kogut–Susskind quark in the strong coupling limit using the tensor renormalization group method. The chiral and nuclear transitions are investigated by calculating the chiral condensate and the quark number density as a function of the chemical potential. For a fixed temporal extent $N_{\tau }=8$, we determine the critical quark masses $m_c^{\chi }$ and $m_c^n$ for the chiral condensate and the quark number density, respectively, at which the first-order phase transition terminates with the vanishing discontinuity in thermodynamic quantities. We find that both quantities at the same quark mass exhibit a discontinuity at the same chemical potential, and the resulting critical quark masses are consistent with each other. We also compare our results for the critical quark masses with those obtained from the Monte Carlo simulation in the dual formulation and from the mean-field analysis. We further confirm the first-order phase transition at finite quark mass on a ${1024}^4$ lattice, which is essentially in the thermodynamic limit at zero temperature, as expected from the mean-field analysis.

The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross-Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f=1$, 2, 3, 4 using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.

The hyperon-antihyperon pairs produced in electron-positron annihilation as a massive two-qubit quantum system can be used to study the quantum correlations at high energies. This paper is theoretically dedicated to how polarization of lepton beams manipulates the Bell nonlocality and entanglement of hyperon pair systems. The response of the Clauser–Horne–Shimony–Holt parameter, concurrence, and negativity to the polarization degree of the beam is numerically calculated by exploiting the joint spin density matrix of hyperon-antihyperon pairs. Different influences of longitudinal and transverse polarization of beams on entanglement are found and compared. The results provide alternative perspectives for the decay of charmonium to hyperon pairs.

In this paper we discuss the multiplicity distribution in the deep inelastic processes in the frame work of high energy QCD. We obtained three results. First, we get the new derivation of the equations for the cross sections of productions of $n$-cut Pomerons in the final states (${\sigma }_n$). These equations coincide with the equations that have been derived using the Abramovsky-Gribov-Kancheli cutting rules but based on the dipole approach to QCD. Second, we developed the homotopy approach for finding the solutions to these equations. It consists with the analytic solution for the first iteration and the converge procedure of calculating the next iterations using computing. Third, we found the analytical solution for ${\sigma }_n$ at large $n\gtrsim N(z)=2N_{0}z\exp (z^2/(2\kappa ))$ with $z=\ln (r^2{Q}_s^2)$. Using this solution we calculate the entropy of the produced gluons at large $z$: $S_E=\ln (N(z))$, where the saturation momentum $Q_s$ and all constants are discussed in the text.

We present a comprehensive study of the two-flavor quark-meson-diquark (QMD) model by comparing a renormalization approach with a renormalization-group (RG) consistent mean-field formulation based on the functional renormalization group (FRG). The renormalized QMD model allows analytical investigations of key quantities such as the zero-temperature diquark gap and the critical temperature for color superconductivity, ultimately reproducing the exact BCS relation in the high-density limit. We carry out the same analysis for different schemes of RG-consistent QMD models. We show that the RG-consistent approach yields a phase diagram and thermodynamic properties qualitatively similar to those of the renormalized model, provided both are embedded within a unified scheme that ensures consistent vacuum properties. In particular, both treatments recover the Stefan-Boltzmann limit at high densities. On the other hand, whether the BCS relation for the critical temperature is satisfied depends on the details of the RG-consistent setup. Our results highlight the relevance of renormalization and RG-consistent methods for accurately capturing the thermodynamics of QMD and related effective models with diquark degrees of freedom.

The tensor-polarized parton density is defined by the forward matrix element of a partonic operator in the $N\to \mathrm{\Delta }$ transition. In this work, we investigate it by employing the large-$N_c$ light-cone wave function derived from the mean-field approach. The mean-field picture is based on low-energy effective dynamics in the large-$N_c$ limit, where the baryon wave function is formulated in the rest frame. By exploiting the covariance of the mean-field solution, we derive the corresponding large-$N_c$ light-cone wave function—decomposed unambiguously into $3Q$, $5Q$, $7Q$, and higher Fock components—in the infinite momentum frame. Evaluating the overlap of these wave functions, we derive an overlap representation of the tensor-polarized parton density in the $N\to \mathrm{\Delta }$ transition and find that the leading contribution arises from the $5Q$ Fock sector. This indicates that the tensor-polarized parton density directly probes the genuine $5Q$ component and is governed by chiral dynamics. Our numerical analysis shows that the $N\to \mathrm{\Delta }$ tensor-polarized parton density is suppressed, consistent with standard large-$N_c$ expectations. Finally, we establish connections among the tensor-polarized parton density, the generalized parton distribution $H_X$, and the energy-momentum tensor form factor $F_4$.

We investigate the production of hyperons, charmed baryons, and potential hadronic molecular states in neutrino-proton (${\overline{\nu }}_{\mu }p$) reaction, a process characterized by a particularly clean final state. Employing effective Lagrangians, chiral perturbation theory, and a hadronic molecular model, we perform theoretical calculations for several relevant channels, including those leading to the formation of the hadronic molecular candidate $(\overline{D}N)$ and $(\overline{D}\mathrm{\Sigma })$. Our results indicate that future neutrino facilities could serve as a complementary platform for exploring exotic baryonic states and provide valuable insights into the dynamics of strong interactions in the strange and charm sectors.

We present a novel realization of Dirac leptogenesis based on the postinflationary reheating phase of the early Universe. An asymmetry generated within the scalar sector via $CP$-violating and out-of-equilibrium inflaton decays is transferred to chiral neutrinos through Yukawa interactions and then to baryons via electroweak sphalerons. We describe in detail a minimal realization of this mechanism that naturally accommodates small neutrino Yukawa couplings and results in contributions to the effective number of relativistic species, $N_{\mathrm{eff}}$, testable in upcoming cosmological observations.

We study bulk two-point correlation functions of a massless scalar field in Jackiw-Teitelboim gravity around the eternal black hole saddle. While same-side correlators exhibit exponential decay, two-sided correlators, at the next-to-leading order in steepest-descent approximation, exhibit a ramp followed by a plateau after the initial semiclassical exponential decay. Our results indicate that the late-time saturation of two-sided correlators is already visible within the perturbative saddle expansion of the bulk path integral, without invoking nonperturbative $e^{-S}$ effects. Finally, we show that the dip time, defined as the minimum of the correlator, grows inversely with the black hole temperature, consistent with expectations from the holographic dual.

We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})⋉{\mathrm{H}}_3$, which arises in the context of quantum gravity. We relate quantum observables—specified by representation-theoretic data—to their classical counterparts using generalized Perelomov coherent states and the framework of Berezin quantization. This procedure links abstract representation-theoretic input to geometric classical observables, such as area. We conclude by applying the formalism to static, spherically symmetric spacetimes admitting a horizon.

We argue that a field theory with a ${\mathbb{Z}}_N$ $p$-form symmetry generically admits, in addition to a Higgs phase and a “confining” phase, a Coulomb phase in which the infrared theory contains Abelian $p$-form electrodynamics, similar to the behavior of the Yang-Mills theory coupled to adjoint or fundamental matter. We illustrate our claim with continuum and lattice examples including 2-group higher gauge theory, effective $p$-form $BF$ theories, and lattice $p$-form electrodynamics.

In this work, we investigate the linear stability of a magnetized Einstein-Maxwell solution describing a static, axially symmetric black hole immersed in a uniform magnetic field $B$. We probe the dynamics of an external charged scalar field through its quasinormal modes (QNMs), combining frequency- and time-domain analyses. We find a critical value of the field charge at which the QNM spectrum exhibits universal power-law scaling with an exponent of approximately $1/2$. This critical behavior admits a simple interpretation in terms of a transition between a confined regime, where waves remain effectively trapped within a region of characteristic size $\sim 1/B$, and a deconfined regime, where the field reaches distances $\gg 1/B$ and the damping rate becomes parametrically small. These results provide qualitative and quantitative insights that may inform more realistic scenarios involving highly magnetized compact objects.

Soft hairs of black holes are the Noether charges associated with the generalized Bondi-Metzner-Sachs symmetries. In this work, the images of soft-haired Kerr black holes are studied. For an eternal black hole, the image is rotated, dilated, and drifting compared to that of the bald counterpart in the celestial plane. The rotation and the dilation are independent of time, while the drifting occurs at a constant speed and in a fixed direction. These effects all depend on angular directions. The soft hair of an astronomical black hole can change due to the emission of gravitational or electromagnetic waves from various physical processes occurring in the vicinity of the horizon. Then, the image roams in the observer’s view, causing the image memory effect, the smoking gun for the existence of soft hair. The magnitude of the image memory effect of a huge, spinning black hole accompanied by a much smaller one is estimated. It turns out that this effect is proportional to the mass of the large black hole, increases with its spin, but decreases with the mass ratio. Due to the limited angular resolution of current and future detectors, this effect is hard to detect if the impact of cosmological expansion is ignored.

Galaxy observations suggest that mergers of supermassive black hole binaries (SMBHBs) are rare events on cosmological scales, with characteristic rates of order one per decade across the observable Universe. In this work, we present a framework to search for merging SMBHBs in pulsar timing array (PTA) data using a physically complete waveform model that includes the late inspiral, merger, ringdown, and gravitational-wave memory. This approach enables a unified treatment of continuous premerger emission and the nonoscillatory memory signal associated with coalescence. Using simulated PTA datasets, we demonstrate a proof of principle for parameter estimation of merging SMBHBs, focusing on representative systems with chirp masses of ${10}^8$ and ${10}^{10}{M}_{\odot }$ at distances of 3 Mpc and 100 Mpc respectively. These signals are distinguishable for a PTA consisting of 25 pulsars observed over 13 years with 100 ns timing precision. For these sufficiently strong signals, we recover the simulated binaries with log Bayes factors exceeding 10, and show that chirp mass and luminosity distance can be jointly constrained with uncertainties governed by the characteristic mass-distance degeneracy of the signal. The sky position uncertainties are of the order of a few degrees, which could potentially enable electromagnetic follow-up and multimessenger observations of SMBHB mergers. We also show that the measurement uncertainties on the parameters of simulated merging binaries depend weakly on the presence of the gravitational wave background with Hellings-Downs correlations in our simulated data. We further demonstrate that commonly used memory burst approximations lead to biased strain amplitudes and inferred source parameters when compared to the full SMBHB waveform, even when optimally tuned. These results establish a pathway toward searching for SMBHB mergers and late-stage inspirals with PTAs using physically complete waveform models, complementing existing searches for continuous gravitational waves.

The “ringdown” stage of gravitational-wave signals from binary black hole mergers, mainly consisting of a superposition of quasinormal modes emitted by the merger remnant, is a key tool to test fundamental physics and to probe black hole dynamics. However, ringdown models are known to be accurate only in the late-time, stationary regime. A key open problem in the field is to understand if these models are robust when extrapolated to earlier times, and if they can faithfully recover a larger portion of the signal. We address this question through a systematic time-domain calculation of the mismatch between nonprecessing, quasicircular ringdown models parametrized by the progenitor binary’s degrees of freedom and full numerical relativity inspiral-merger-ringdown waveforms from the simulating extreme spacetimes (SXS) simulation catalog. For the best-performing models, the mismatch is typically in the range $[{10}^{-6},{10}^{-4}]$ for the $(\ell ,|m|)=(2,2)$ harmonic, and $[{10}^{-4},{10}^{-2}]$ for higher-order modes. Our findings inform ongoing observational searches for quasinormal modes, and underscore the need for improved modeling of higher-order modes to meet the sensitivity requirements of future gravitational-wave detectors.

We present a comprehensive analysis of late-time tails in gravitational radiation from merging spin-aligned eccentric binary black holes, using high-accuracy point-particle black hole perturbation theory simulations. We simulate the late-time evolution of 15 binary black hole mergers with mass ratio $q=1000$, dimensionless spins $\chi =[-0.9,-0.6,0.0,0.6,0.9]$, and eccentricity at the last stable orbit $e_{\mathrm{LSO}}=[0.8,0.9,0.95]$. We track the tail amplitudes and exponents up to a retarded time coordinate $t=9000M$ after merger for the six spin-weighted spherical harmonic modes (2, 1), (2, 2), (3, 2), (3, 3), (4, 3), and (4, 4) employing both frequentist and Bayesian approaches. We note that the tails are increasingly pronounced for binaries with high eccentricity $e_{\mathrm{LSO}}$ and large negative spin $\chi$. We find that the overall late-time exponents closely approach their predicted asymptotic values ($p=-\ell -4$ for Weyl curvature scalar ${\psi }_{4,\ell m}$ where $\ell$ is the spin-weighted spherical harmonic index), while estimates restricted to the latest portion of the data exactly recover them. We further verify numerically that modes with the same spherical index $\ell$ share identical tail exponents, while variations in $m$ do not affect the tail behavior. Additionally, for completeness, we provide a brief exploration of the intermediate behavior of the tails. Our analysis framework is publicly available through the gwtails python package.

We study the capability of future space-based gravitational-wave (GW) detectors to constrain supermassive black hole (SMBH) properties through observations of inspiraling stellar-mass binary black holes (BBHs) orbiting them. Focusing on stable hierarchical triple systems, we model the BBH motion in Kerr spacetime and compute the modulated GW signals using the post Newtonian waveform combined with moving-source transformation. Based on the LISA configuration and second-generation time delay interferometry technology, we estimate parameter uncertainties with the Fisher information matrix. Our results show that the outer semimajor axis has the strongest influence on parameter precision, while the SMBH spin and eccentricity mainly affect their own uncertainties. For high-SNR signals, the SMBH mass and orbital parameters can be measured with relative uncertainties on the order of ${10}^{-5}$, while the spin magnitude and its orientation can be constrained to within a few percentages. Applying the method to an M87*-like system, GW observations provide more precise measurements of the SMBH mass and spin compared with current electromagnetic observations, highlighting the potential of space-based GW astronomy to probe SMBH properties with high accuracy.

Gravitational wave echoes offer a unique probe of the near-horizon structure of astrophysical black holes, beyond the standard “black hole spectroscopy.” Theoretical waveform predictions, however, remain uncertain, motivating robust searches that avoid specific echo modeling. We present a model-agnostic search framework targeting long-lived quasinormal modes (QNMs) expected from strong interior reflection. By employing a generalized phase-marginalized likelihood that coherently combines data for each QNM across a detector network, our method enhances sensitivity to the signals. To handle real detector noise, we implement an optimized notching procedure to suppress instrumental spectral lines and refine the Bayesian parameter settings. We validate the performance of this framework using injection studies on O1 background data, demonstrating reliable signal recovery in realistic noise conditions. We then apply this method to three binary black hole merger events with high ringdown SNRs: GW150914 from O1, GW231226 from O4a, and the recently reported O4 event GW250114. No statistically significant evidence for postmerger echoes is found. Consequently, we derive 90% upper limits on the network SNR and the average initial strain amplitude of the long-lived QNMs. These results provide model-agnostic constraints on late-time echoes from LVK data, complementing existing searches for other echo signatures.

Tomographic weak lensing surveys contain intrinsic symmetries that depend solely on the geometric structure of the Universe. These symmetries can be revealed through null tests and verifying their validity provides constraints on cosmological parameters that govern the background evolution—particularly the redshift dependence of the angular diameter distance. This forms the foundation of the tomographic cosmic shear nulling test introduced in this work. We describe how this test can be implemented, what aspects of cosmology it can constrain, and its specific efficiency in doing so. We also assess its sensitivity to astrophysical effects—such as magnification bias and reduced shear corrections—as well as to observational systematics, including errors in the mean redshift of source bins. Our results show that, in a survey configuration comparable to that of Euclid, this null test can yield complementary constraints on key cosmological parameters such as ${\mathrm{\Omega }}_{\mathrm{m}},{\mathrm{w}}_0$. However, due to its subdominant constraining power compared to standard $3\times 2\mathrm{pt}$ analysis and through the identification of a required precision of order ${10}^{-3}$ on the mean redshift of the bins, we conclude that nulling would better be used as a photometric redshift calibration probe or consistency check. In combination with standard weak lensing and galaxy clustering analysis, it would then offer a promising route to better control systematics and improve the precision of future cosmological measurements.