In the context of bottom-up AdS/QCD models, we discuss how the configurational entropy can describe heavy non-$q\overline{q}$ states. Using the nonquadratic softwall model, introduced to describe nonlinear Regge trajectories, we parametrize different multiquark and exotic meson structures to describe $Z_c$, $\psi$, and $Z_b$ states as non-$q\overline{q}$ hadrons in terms of stability. We found that $Z_c$ is better described as a hybrid meson with one gluon tube, $\psi$ as hadrocharmonium, and $Z_b$ as hadronic molecule.

We construct novel scalarized black hole (BH) solutions beyond the general relativity (GR) framework. These scalarized BH solutions are extended from the Schwarzschild one and the non-Schwarzschild one in the pure Einstein-Weyl gravity. By studying the BH entropy and free energy, we demonstrate that the scalarized BH extending from the Schwarzschild one exhibits thermodynamically preferred. We obtain these novel solutions by directly solving the full fourth-order equations of motion. This narrows the problematic solution space obtained by commonly adopted second-order reduction to physically valid spaces. Our findings also unveil the evasion of the no-hair theorem within the realm of higher-derivative gravity.

We observe the process $\mathrm{\Upsilon }(2S)\to D_s^{(*)+}{D}_{sJ}^{-}$ and continuum production $e^{+}{e}^{-}\to D_s^{(*)+}{D}_{sJ}^{-}$ at $\sqrt{s}=10.52\mathrm{GeV}$ (and their charge conjugates) using the data samples collected by the Belle detector at KEKB, where $D_{sJ}^{-}$ is $D_{s1}(2536{)}^{-}$ or $D_{s2}^{*}(2573{)}^{-}$. Both $D_{sJ}^{-}$ states are identified through their decay into $\overline{K}{\overline{D}}^{(*)}$. We measure the products of branching fractions $\mathcal{B}(\mathrm{\Upsilon }(2S)\to D_s^{(*)+}{D}_{sJ}^{-})\mathcal{B}(D_{sJ}^{-}\to \overline{K}{\overline{D}}^{(*)})$ and the Born cross sections ${\sigma }^{\text{Born}}(e^{+}{e}^{-}\to D_s^{(*)+}{D}_{sJ}^{-})\mathcal{B}(D_{sJ}^{-}\to \overline{K}{\overline{D}}^{(*)})$, and then compare the ratios $R_1\equiv \mathcal{B}(\mathrm{\Upsilon }(2S)\to D_s^{(*)+}{D}_{sJ}^{-})/\mathcal{B}(\mathrm{\Upsilon }(2S)\to {\mu }^{+}{\mu }^{-})$ for $\mathrm{\Upsilon }(2S)$ decays and $R_2\equiv {\sigma }^{\text{Born}}(e^{+}{e}^{-}\to D_s^{(*)+}{D}_{sJ}^{-})/{\sigma }^{\text{Born}}(e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})$ for continuum production. We obtain $R_1/R_2=9.7\pm 2.3\pm 1.1$, $6.8\pm 2.1\pm 0.8$, $10.2\pm 3.3\pm 2.5$, and $3.4\pm 2.1\pm 0.8$ for the $D_s^{+}{D}_{s1}(2536{)}^{-}$, $D_s^{*+}{D}_{s1}(2536{)}^{-}$, $D_s^{+}{D}_{s2}^{*}(2573{)}^{-}$, and $D_s^{*+}{D}_{s2}^{*}(2573{)}^{-}$ final states in the $D_{sJ}^{-}\to K^{-}{\overline{D}}^{(*)0}$ modes, respectively. The measured $R_1/R_2$ values indicate that the strong decay dominates in $\mathrm{\Upsilon }(2S)\to D_s^{(*)+}{D}_{sJ}^{-}$ processes. We also measure the ratios of branching fractions $\mathcal{B}(D_{s1}(2536{)}^{-}\to K_S^0{D}^{*}(2010{)}^{-})/\mathcal{B}(D_{s1}(2536{)}^{-}\to K^{-}{D}^{*}(2007{)}^0)=0.48\pm 0.07\pm 0.02$ and $\mathcal{B}(D_{s2}^{*}(2573{)}^{-}\to K_S^0{D}^{-})/\mathcal{B}(D_{s2}^{*}(2573{)}^{-}\to K^{-}{D}^0)=0.49\pm 0.10\pm 0.02$, which are consistent with isospin symmetry. The second ratio is the first measurement of this quantity. Here, the first uncertainties are statistical and the second are systematic.

Quantum matrix geometry is the underlying geometry of M(atrix) theory. Expanding upon the idea of level projection, we propose a quantum-oriented noncommutative scheme for generating the matrix geometry of the coset space $G/H$. We employ this novel scheme to unveil unexplored matrix geometries by utilizing gauged quantum mechanics on higher dimensional spheres. The resultant matrix geometries manifest as pure quantum Nambu geometries: Their noncommutative structures elude capture through the conventional commutator formalism of Lie algebra, necessitating the introduction of the quantum Nambu algebra. This matrix geometry embodies a one-dimension-lower quantum internal geometry featuring nested fuzzy structures. While the continuum limit of this quantum geometry is represented by overlapping classical manifolds, their fuzzification cannot reproduce the original quantum geometry. We demonstrate how these quantum Nambu geometries give rise to novel solutions in Yang-Mills matrix models, exhibiting distinct physical properties from the known fuzzy sphere solutions.

We investigate the monotonicity of the renormalization group (RG) flow from the perspectives of nonequilibrium thermodynamics. Applying the Martin-Siggia-Rose formalism to the Wilsonian RG transformation, we incorporate the RG flow equations manifestly in an effective action, where all coupling functions are dynamically promoted. As a result, we obtain an emergent holographic dual effective field theory, where an extra dimension appears from the Wilsonian RG transformation. We observe that Becchi-Rouet-Stora-Tyutin (BRST)-type transformations play an important role in the bulk effective action, which give rise to novel Ward identities for correlation functions between the renormalized coupling fields. As generalized fluctuation-dissipation theorems in the semiclassical nonequilibrium dynamics can be understood from the Ward identities of such BRST symmetries, we find essentially the same principle for the RG flow in the holographic dual effective field theory. Furthermore, we discuss how these “nonequilibrium work identities” can be related to the monotonicity of the RG flow, for example, the $c$-theorem. In particular, we introduce an entropy functional for the dynamical coupling field and show that the production rate of the total entropy functional is always positive, indicating the irreversibility of the RG flow.

We quantize the ModMax oscillator, which is the dimensional reduction of the modified Maxwell theory to one spacetime dimension. We show that the propagator of the ModMax oscillator satisfies a differential equation related to the Laplace equation in cylindrical coordinates, and we obtain expressions for the classical and quantum partition functions of the theory. To do this, we develop general results for deformations of quantum-mechanical theories by functions of conserved charges. We show that canonical quantization and path integral quantization of such deformed theories are equivalent only if one uses the phase space path integral; this gives a precise quantum analog of the statement that classical deformations of the Lagrangian are equivalent to those of the Hamiltonian.

We consider the fermion mass renormalization due to the vector boson exchange within mesodynamics with nucleon and $\rho$ meson fields as well as quantum electrodynamics with electron and photon fields. The method of unitary clothing transformations is used to handle the so-called clothed particle representation that allows us to get rid of mass counterterms directly in the Hamiltonian. Thus, they can no longer appear in the $S$-matrix. Special attention is paid to the cancellation of the so-called contact terms that are inevitable in models with vector bosons. Within this formalism, the second-order mass shifts are derived. They are expressed through the corresponding three-dimensional integrals whose integrands depend on certain covariant combinations of the relevant three-momenta. Our results are proved to be particle-momentum independent and compared with ones obtained by Feynman techniques.

We discuss the generalization of the local renormalization group approach to theories in which Weyl symmetry is gauged. These theories naturally correspond to scale-invariant—rather than conformal-invariant—models in the flat-space limit. We argue that this generalization can be of use when discussing the issue of scale vs conformal invariance in quantum and statistical field theories. The application of Wess-Zumino consistency conditions constrains the form of the Weyl anomaly and the beta functions in a nonperturbative way. In this work, we concentrate on two-dimensional models including also the contributions of the boundary. Our findings suggest that the renormalization group flow between scale-invariant theories differs from the one between conformal theories because of the presence of a new charge that appears in the anomaly. It does not seem to be possible to find a general scheme for which the new charge is zero, unless the theory is conformal in flat space. Two illustrative examples involving flat space’s conformal- and scale-invariant models that do not allow for a naive application of the standard local treatment are given.

We study nonlinear matter models compatible with radiative Robinson-Trautman spacetimes and analyze their stability and well-posedness. The results lead us to formulate a conjecture relating the (in)stability and well/ill-posedness to the character of singularity appearing in the solutions. We consider two types of nonlinear electrodynamics models, namely we provide a radiative ModMax solution and extend recent results for the RegMax model by considering the magnetically charged case. In both cases, we investigate linear perturbations around stationary spherically symmetric solutions to determine the stability and principal symbol of the system to argue about well-posedness of these geometries. Additionally, we consider a nonlinear sigma model as a source for Robinson–Trautman geometry. This leads to stationary solutions with toroidal (as opposed to spherical) topology thus demanding modification of the analysis.

We study various aspects of higher-curvature theories of gravity built from contractions of the metric, the Riemann tensor, and the covariant derivative, $\mathcal{L}(g^{ab},R_{abcd},{\nabla }_a)$. We characterize the linearized spectrum of these theories and compute the modified Newton potential in the general case. Then, we present the first examples of generalized quasitopological (GQT) gravities involving covariant derivatives of the Riemann tensor. We argue that they always have second-order equations on maximally symmetric backgrounds. Focusing on four spacetime dimensions, we find new densities of that type involving eight and ten derivatives of the metric. In the latter case, we find new modifications of the Schwarzschild black hole. These display thermodynamic properties which depart from the ones of polynomial GQT black holes. In particular, the relation between the temperature and the mass of small black holes, $T\sim M^{1/3}$, which universally holds for general polynomial GQT modifications of Einstein gravity, gets modified in the presence of the new density with covariant derivatives to $T\sim M^3$. Finally, we consider brane-world gravities induced by Einstein gravity in the AdS bulk. We show that the effective quadratic action for the brane-world theory involving arbitrary high-order terms in the action can be written explicitly in a closed form in terms of Bessel functions. We use this result to compute the propagator of metric perturbations on the brane and its pole structure in various dimensions, always finding infinite towers of ghost modes, as well as tachyons and more exotic modes in some cases.

The loop quantization of the conformal Brans-Dicke cosmology is explored in the spatially flat and Bianchi-I setting. The scalar and conformal constraints governing the canonical model are quantized using the loop techniques. The physical Hilbert space of quantum spacetimes satisfying both quantum constraints is then obtained by incorporating the quantum geometric features. The Schrödinger cosmic evolutions are derived with the relational Heisenberg observables describing the dynamical degrees of freedom with respect to the chosen reference degrees of freedom, with the latter providing the physical coordinates for the spatial hypersurfaces and the conformal scales. We show that the emerging Schrödinger theories contain not only the loop quantum cosmology of general relativity, but also that of the so-called shape dynamics. The exact dictionary between the two theories is achieved via the underlying physical Hilbert space possessing the additional (loop-corrected) conformal symmetry.

A major science goal of gravitational-wave (GW) observations is to probe the nature of gravity and constrain modifications to general relativity. An established class of modified gravity theories are scalar-tensor models, which introduce an extra scalar degree of freedom. This affects the internal structure of neutron stars (NSs), as well as their dynamics and GWs in binary systems, where distinct novel features can arise from the appearance of scalar condensates in parts of the parameter space. To improve the robustness of the analyses of such GW events requires advances in modeling internal-structure-dependent phenomena in scalar-tensor theories. We develop an effective description of potentially scalarized NSs on large scales, where information about the interior is encoded in characteristic Love numbers or, equivalently, tidal deformabilities. We demonstrate that three independent tidal deformabilities are needed to characterize the configurations—a scalar, a tensor, and a novel “mixed” parameter—and develop the general methodology to compute these quantities. We also present case studies for different NS equations of state and scalar properties and provide the mapping between the deformabilities in different frames often used for calculations. Our results have direct applications for future GW tests of gravity and studies of potential degeneracies with other uncertain physics such as the equation of state or presence of dark matter in NS binary systems.

Recently, various types of the regular black hole model are reintroduced as the solution of the Einstein equations coupled with nonlinear electrodynamics (NED). In NED, it is known that photons do not propagate along the null geodesics of the spacetime geometry, but of so-called effective geometry, which suggests the possibility of so-called “faster/slower than light” photons. We study the relation between the causality of photons and the dominant energy condition (DEC) in some static and spherically symmetric black hole spacetimes in NED. We show that if photon trajectories with a nonzero angular momentum are timelike in the spacetime geometry, DEC is always satisfied in static and spherically symmetric spacetimes in any NED that admits the Maxwell limit, and vice versa, at least, in the weak field limit. Thus, this implies that in such NED, the violation of DEC admits the existence of faster than light photons.

We study the collisions of two scalar wave packets in the asymptotically flat spacetime and asymptotically anti–de Sitter spacetime in spherical symmetry. An energy transfer formula is obtained, $y=C{m}_i{m}_o/r$, where $y$ is the transferred energy in the collisions of the two wave packets; $m_i$ and $m_o$ are the Misner-Sharp energies for the ingoing and outgoing wave packets, respectively; $r$ is the areal radius and collision place; and $C=1.873$ and $C=1.875$ for the asymptotically flat spacetime and asymptotically anti–de Sitter spacetime circumstances, respectively. The formula is universal, independent of the initial profiles of the scalar fields.

The hyperbolic formulations of numerical relativity due to Baumgarte, Shapiro, Shibata, and Nakamura (BSSN) and Nagy Ortiz and Reula (NOR), among others, achieve stability through the effective embedding of general relativity within the larger Z4 system. In doing so, various elliptic constraints are promoted to dynamical degrees of freedom, permitting the advection of constraint violating modes. Here we demonstrate that it is possible to achieve equivalent performance through a modification of fully covariant and conformal Z4 (FCCZ4) wherein constraint violations are coupled to a reference metric completely independently of the physical metric. We show that this approach works in the presence of black holes and holds up robustly in a variety of spherically symmetric simulations including the critical collapse of a scalar field. We then demonstrate that our formulation is strongly hyperbolic through the use of a pseudodifferential first order reduction and compare its hyperbolicity properties to those of FCCZ4 and generalized BSSN (GBSSN). Our present approach makes use of a static Lorentzian reference metric and does not appear to provide significant advantages over FCCZ4. However, we speculate that dynamical specification of the reference metric may provide a means of exerting greater control over constraint violations than what is provided by current BSSN-type formulations.

The detection of low-frequency gravitational waves astronomy has marked the advent of a new era in the domain of astrophysics and general relativity. Using the framework of interaction between gravitational waves (GWs) and a point two-particles-like detector, within a linearized gravity approach, we propose a toy detector model whose quantum state is being investigated at a low frequency of GWs. The detector is in simultaneous interaction with GWs and an external time-dependent (tuneable) two-dimensional harmonic potential. We observe that the interaction with low-frequency GWs naturally provides adiabatic approximation in the calculation and thereby can lead to a quantal geometric phase in the quantum states of the detector. Moreover, this can be controlled by tuning the frequency of the external harmonic potential trap. We argue that such a geometric phase detection may serve as a manifestation of the footprint of GWs. More importantly, our theoretical model may be capable of providing a layout for the detection of very-small-frequency GWs through the Berry phase.

The latest pulsar timing array data reveal evidence of nanohertz gravitational waves (GWs), which have been explained by both cosmological and astrophysical sources. However, current observations lack the precision needed to differentiate between different models from the spectral index. We find that the cosmological GW sources, including bubble collisions, sound waves, domain walls, condensate fragmentations, and primordial curvature perturbations, induce large energy density perturbations so that most dark matter will exist in gravitationally self-bound subhalos. Then, the observation of such substructures of dark matter can serve as a novel independent method to confirm or exclude the cosmological GW sources.

Cosmological simulations for cold dark matter (DM) indicate that a large number of streams might exist in our Galaxy. The present work incorporates gravitational focusing (GF) effects on streaming DM constituents by the Sun and the Earth preceding their encounter with Earth bound detectors. For streaming DM, the GF gives rise to spatiotemporal flux enhancements of orders of magnitude above the nominal DM density. Remarkably, due to Earth’s rotation the derived flux enhancements appear as transient signals lasting about 10 seconds repeating daily for days or weeks. This work presents a novel opportunity for DM signal detection and identification, and the present simulation can be applied to any kind of invisible matter entering the Solar System.

Parameter estimation plays a critical role in the detection of gravitational waves, and for space-based detectors, time delay interferometry is indispensable to ensure mission success. This paper employs the Fisher matrix method to systematically analyze the parameter estimation and localization capabilities of TianQin and LISA for monochromatic sources and coalescing supermassive black hole binaries under various time-delay interferometry combinations. For monochromatic sources, the accuracy of parameter estimation for TianQin and LISA significantly improves within one year of observation time, followed by a gradual increase due to signal-to-noise ratio effects. The improvement in localization with multichannel data stabilizes at 2–4 times that of single-channel data after the observation time exceeds one year. The coalescence of supermassive black hole binaries is investigated by considering 30-day inspiral-merger-ringdown signals that incorporate higher-order modes. It is observed that the inclusion of higher modes enhances the localization advantages provided by a multichannel network. Specifically, for TianQin, the multichannel network yields significant improvements in localization accuracy for binaries with a total mass of $4\times {10}^6{M}_{\odot }$, up to an order of magnitude. In contrast, for LISA, the gains increase with mass, ranging from several times at $2\times {10}^5{M}_{\odot }$ to more than 2 orders of magnitude at $4\times {10}^7{M}_{\odot }$.

In this paper, we investigate the dynamics of a binary system that orbits a rotating supermassive black hole. Our approach employs Fermi-Walker transport to construct a local inertial reference frame, and to set up a Newtonian binary system. We consider a scenario in which a circular geodesic observer is positioned around a Kerr black hole, and thereby derive the equations of motion governing the binary system. To eliminate the interaction terms between the c.m. of the binary and its relative coordinates, we introduce a small acceleration for the observer. This adjustment leads to the c.m. closely following the observer’s orbit, deviating from a circular geodesic. Here, we first focus on elucidating the stability conditions in a hierarchical triple system. Subsequently, we discuss the phenomenon of von Zeipel-Lidov-Kozai oscillations, which manifest when the binary system is compact and the initial inclination exceeds a critical angle. In hard binary systems, these oscillations exhibit regular behavior, while in soft binary systems, they exhibit a chaotic character, characterized by irregular periods and amplitudes, albeit remaining stable. Additionally, we observe an orbital flip under circumstances of large initial inclination. As for the motion of the c.m., we observe deviations from a purely circular orbit that transform into stable yet chaotic oscillations characterized by minute amplitude variations.