The low-energy limit of the massless two-loop five-point amplitudes for both type IIA and type IIB superstrings is computed with the pure spinor formalism and its overall coefficient determined from first principles. For the type IIB theory, the five-graviton amplitude is found to be proportional to its tree-level counterpart at the corresponding order in ${\alpha }^{\prime }$. Their ratio ties in with expectations based on S-duality since it matches the same modular function $E_{5/2}$ which relates the two-loop and tree-level four-graviton amplitudes. For R-symmetry violating states, the ratio between tree-level and two-loop amplitudes at the same ${\alpha }^{\prime }$-order carries an additional factor of $-3/5$. Its $S$-duality origin can be traced back to a modular form derived from $E_{5/2}$.

We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid’s undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein’s equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to the Taylor series with respect to the eccentricity of the ellipsoid and discuss their practical applications for geodetic constants and relations adopted in fundamental astronomy.

We investigate the interior dynamics of accreting black holes in Eddington-inspired Born-Infeld gravity using the homogeneous approximation and taking charge as a surrogate for angular momentum, showing that accretion can have an enormous impact on their inner structure. We find that, unlike in general relativity, there is a minimum accretion rate below which the mass inflation instability, which drives the center-of-mass streaming density to exponentially high values in an extremely short interval of time, does not occur. We further show that, above this threshold, mass inflation takes place inside black holes much in the same way as in general relativity, but is brought to a halt at an energy density which is, in general, much smaller than the fundamental energy density of the theory. We conjecture that some of these results may be a common feature of modified gravity theories in which significant deviations from general relativity manifest themselves at high densities.

A general formula for the electromagnetic energy radiated by a rapidly rotating magnetic dipole in arbitrary motion is obtained. For a pulsar orbiting in a binary system, it is shown that the electromagnetic radiation produced by the orbital motion is usually weaker than the gravitational radiation, but not entirely negligible for general relativistic corrections.

Binary neutron star (NS) mergers are strong gravitational-wave (GW) sources and the leading candidates to interpret short-duration gamma-ray bursts (SGRBs). Under the assumptions that SGRBs are produced by double neutron star mergers and that the x-ray plateau followed by a steep decay as observed in SGRB x-ray light curves marks the collapse of a supramassive neutron star to a black hole (BH), we use the statistical observational properties of Swift SGRBs and the mass distribution of Galactic double neutron star systems to place constraints on the neutron star equation of state (EoS) and the properties of the post-merger product. We show that current observations already impose the following interesting constraints. (1) A neutron star EoS with a maximum mass close to a parametrization of $M_{\max }=2.37M_{\odot }(1+1.58\times {10}^{-10}{P}^{-2.84})$ is favored. (2) The fractions for the several outcomes of NS-NS mergers are as follows: $\sim 40\%$ prompt BHs, $\sim 30\%$ supramassive NSs that collapse to BHs in a range of delay time scales, and $\sim 30\%$ stable NSs that never collapse. (3) The initial spin of the newly born supramassive NSs should be near the breakup limit ($P_i\sim 1\mathrm{ms}$), which is consistent with the merger scenario. (4) The surface magnetic field of the merger products is typically $\sim {10}^{15}\mathrm{G}$. (5) The ellipticity of the supramassive NSs is $\epsilon \sim (0.004-0.007)$, so that strong GW radiation is released after the merger. (6) Even though the initial spin energy of the merger product is similar, the final energy output of the merger product that goes into the electromagnetic channel varies in a wide range from several ${10}^{49}$ to several ${10}^{52}\mathrm{erg}$, since a good fraction of the spin energy is either released in the form of GWs or falls into the black hole as the supramassive NS collapses.

Gravitational waves from binary neutron star (BNS) and black hole/neutron star (BHNS) inspirals are primary sources for detection by the Advanced Laser Interferometer Gravitational-Wave Observatory. The tidal forces acting on the neutron stars induce changes in the phase evolution of the gravitational waveform, and these changes can be used to constrain the nuclear equation of state. Current methods of generating BNS and BHNS waveforms rely on either computationally challenging full 3D hydrodynamical simulations or approximate analytic solutions. We introduce a new method for computing inspiral waveforms for BNS/BHNS systems by adding the post-Newtonian (PN) tidal effects to full numerical simulations of binary black holes (BBHs), effectively replacing the nontidal terms in the PN expansion with BBH results. Comparing a waveform generated with this method against a full hydrodynamical simulation of a BNS inspiral yields a phase difference of $<1$ radian over $\sim 15$ orbits. The numerical phase accuracy required of BNS simulations to measure the accuracy of the method we present here is estimated as a function of the tidal deformability parameter $\lambda$.

We discuss Stueckelberg massive electromagnetism on an arbitrary four-dimensional curved spacetime and, in particular, (i) the gauge invariance of the classical theory and its covariant quantization; (ii) the wave equations for the massive spin-1 field $A_{\mu }$, for the auxiliary Stueckelberg scalar field $\mathrm{\Phi }$ and for the ghost fields $C$ and $C^{*}$; (iii) Ward identities; (iv) the Hadamard representation of the various Feynman propagators and the covariant Taylor series expansions of the corresponding coefficients. This permits us to construct, for a Hadamard quantum state, the expectation value of the renormalized stress-energy tensor associated with the Stueckelberg theory. We provide two alternative but equivalent expressions for this result. The first one is obtained by removing the contribution of the “Stueckelberg ghost” $\mathrm{\Phi }$ and only involves state-dependent and geometrical quantities associated with the massive vector field $A_{\mu }$. The other one involves contributions coming from both the massive vector field and the auxiliary Stueckelberg scalar field, and it has been constructed in such a way that, in the zero-mass limit, the massive vector field contribution reduces smoothly to the result obtained from Maxwell’s theory. As an application of our results, we consider the Casimir effect outside a perfectly conducting medium with a plane boundary. We discuss the results obtained using Stueckelberg but also de Broglie-Proca electromagnetism, and we consider the zero-mass limit of the vacuum energy in both theories. We finally compare the de Broglie-Proca and Stueckelberg formalisms and highlight the advantages of the Stueckelberg point of view, even if, in our opinion, the de Broglie-Proca and Stueckelberg approaches of massive electromagnetism are two faces of the same field theory.

We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories, in general, include a graviton, a dilaton and a rank-two antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via Bern-Carrasco-Johansson duality can be made more manifest in this formulation.

We consider the possibility of inflationary magnetogenesis due to dynamical couplings of the electromagnetic fields to gravity. We find that large primordial magnetic fields can be generated during inflation without the strong coupling problem, backreaction problem, or curvature perturbation problem, which seed large-scale magnetic fields with observationally interesting strengths.

Light scalar fields such as axions and string moduli can play an important role in early-universe cosmology. However, many factors can significantly impact their late-time cosmological abundances. For example, in cases where the potentials for these fields are generated dynamically—such as during cosmological mass-generating phase transitions—the duration of the time interval required for these potentials to fully develop can have significant repercussions. Likewise, in scenarios with multiple scalars, mixing amongst the fields can also give rise to an effective timescale that modifies the resulting late-time abundances. Previous studies have focused on the effects of either the first or the second timescale in isolation. In this paper, by contrast, we examine the new features that arise from the interplay between these two timescales when both mixing and time-dependent phase transitions are introduced together. First, we find that the effects of these timescales can conspire to alter not only the total late-time abundance of the system—often by many orders of magnitude—but also its distribution across the different fields. Second, we find that these effects can produce large parametric resonances which render the energy densities of the fields highly sensitive to the degree of mixing as well as the duration of the time interval over which the phase transition unfolds. Finally, we find that these effects can even give rise to a “reoverdamping” phenomenon which causes the total energy density of the system to behave in novel ways that differ from those exhibited by pure dark matter or vacuum energy. All of these features therefore give rise to new possibilities for early-universe phenomenology and cosmological evolution. They also highlight the importance of taking into account the time dependence associated with phase transitions in cosmological settings.

Evaluation of the angular distribution function of particles scattered in an amorphous medium is improved by deforming the integration path in the Fourier integral representation into the complex plane. That allows us to present the distribution function as a sum of two positive components, soft and hard, the soft component being close to a Gaussian, and the hard component vanishing in the forward direction, while including the Rutherford asymptotics and all the power corrections to it at large scattering angles. Detailed properties of these components, and their interplay at intermediate deflection angles are discussed. Comparison with the Molière theory is given.

We present a unified model describing electroweak properties of the $\pi$ and $\rho$ mesons. Using a general method of the relativistic parametrization of matrix elements of local operators, adjusted for the nondiagonal in the total angular momentum case, we calculate the $\rho$-meson lepton-decay constant $f_{\rho }$ using the same parameters of free constituent quarks that have ensured exclusively good results for the $\pi$ meson previously. The only free parameter, characterizing quark interactions, which include an additional spin-spin contribution and hence differ from the $\pi$-meson case, is fixed by matching the decay constant to its experimental value. The mean square charge radius is calculated, $⟨r_{\rho }^2⟩=(0.56\pm 0.04){\mathrm{fm}}^2$. This result confirms, for the $\rho$-meson case, the conjecture of equality between electromagnetic and strong radii of hadrons. This conjecture was tested previously for proton, $\pi$ and $K$ mesons.

Collider experiments provide an opportunity to shed light on dark matter (DM) self-interactions. In this work, we study the possibility of generating DM bound states—the Darkonium—at the LHC and discuss how the annihilation decay of the Darkonium produces force carriers. We focus on two popular scenarios that contain large DM self-couplings: the Higgsinos in the $\lambda \text{−}\mathrm{SUSY}$ model and the self-interacting DM (SIDM) framework. After forming bound states, the DM particles annihilate into force mediators, which decay into the standard model particles either through a prompt or displaced process. This generates interesting signals for the heavy resonance search. We calculate the production rate of bound states and study the projected future constraints from the existing heavy resonance searches.

We evaluate the third- and fourth-order baryon, charge and strangeness susceptibilities near a chiral critical point using the Nambu-Jona-Lasinio model. We identify robust qualitative behaviors of the susceptibilities along hypothetical freeze-out lines that agree with previous model studies. Quantitatively, baryon number fluctuations are the largest in magnitude and thus offer the strongest signal when freeze-out occurs farther away from a critical point. Charge and strangeness susceptibilities also diverge at a critical point, but the area where the divergence dominates is smaller, meaning freeze-out must occur closer to a critical point for a signal to be visible in these observables. In the case of strangeness, this is attributable to the relatively large strange-quark mass. Plotting the third- and fourth-order susceptibilities against each other along the freeze-out line exhibits clearly their nonmontonicity and robust features.

We examine the validity of the generalized factorization method and calculate the angular correlations in the charmful three-body baryonic decays of ${\overline{B}}^0\to \mathrm{\Lambda }\overline{p}{D}^{(*)+}$. With the timelike baryonic form factors newly extracted from the measured baryonic $B$ decays, we obtain $\mathcal{B}({\overline{B}}^0\to \mathrm{\Lambda }\overline{p}{D}^{+},\mathrm{\Lambda }\overline{p}{D}^{*+})=(1.85\pm 0.30,2.75\pm 0.24)\times {10}^{-5}$ to agree with the recent data from the Belle Collaboration, which demonstrates that the theoretical approach based on the factorization still works well. For the angular distribution asymmetries, we find ${\mathcal{A}}_{\theta }({\overline{B}}^0\to \mathrm{\Lambda }\overline{p}{D}^{+},\mathrm{\Lambda }\overline{p}{D}^{*+})=(-0.030\pm 0.002,+0.150\pm 0.000)$, which are consistent with the current measurements. Moreover, we predict that ${\mathcal{A}}_{\theta }({\overline{B}}^0\to p\overline{p}{D}^0,p\overline{p}{D}^{*0})=+0.04\pm 0.01$. Future precise explorations of these angular correlations at Belle and LHCb as well as super-Belle are important to justify the present factorization approach in the charmful three-body baryonic decays.

A search is presented for the production of both first- and second-generation scalar leptoquarks with a final state of either two electrons and one jet or two muons and one jet. The search is based on a data sample of proton-proton collisions at center-of-mass energy $\sqrt{s}=8\mathrm{TeV}$ recorded with the CMS detector and corresponding to an integrated luminosity of $19.6{\mathrm{fb}}^{-1}$. Upper limits are set on both the first- and second-generation leptoquark production cross sections as functions of the leptoquark mass and the leptoquark couplings to a lepton and a quark. Results are compared with theoretical predictions to obtain lower limits on the leptoquark mass. At 95% confidence level, single production of first-generation leptoquarks with a coupling and branching fraction of 1.0 is excluded for masses below 1730 GeV, and second-generation leptoquarks with a coupling and branching fraction of 1.0 is excluded for masses below 530 GeV. These are the best overall limits on the production of first-generation leptoquarks to date.

A search for pair production of first and second generation leptoquarks is performed in final states containing either two charged leptons and two jets, or one charged lepton, one neutrino and two jets, using proton-proton collision data at $\sqrt{s}=8\mathrm{TeV}$. The data, corresponding to an integrated luminosity of $19.7{\mathrm{fb}}^{-1}$, were recorded with the CMS detector at the LHC. First-generation scalar leptoquarks with masses less than 1010 (850) GeV are excluded for $\beta =1.0(0.5)$, where $\beta$ is the branching fraction of a leptoquark decaying to a charged lepton and a quark. Similarly, second-generation scalar leptoquarks with masses less than 1080 (760) GeV are excluded for $\beta =1.0(0.5)$. Mass limits are also set for vector leptoquark production scenarios with anomalous vector couplings, and for R-parity violating supersymmetric scenarios of top squark pair production resulting in similar final-state signatures. These are the most stringent limits placed on the masses of vector leptoquarks and RPV top squarks to date.

In the Lorentzian $\mathrm{AdS}/\mathrm{CFT}$ correspondence, CFTs are identified by asymptotic boundary surfaces and the boundary conditions imposed on those surfaces. However, AdS can be foliated in various ways to give different boundaries. We show that the CFTs obtained using certain distinct foliations are different. This happens because the asymptotic region of a foliation overlaps with the deep interior region of another. In particular, we focus on the CFTs defined on surfaces of large constant radius in global coordinates, Rindler-AdS coordinates, and Poincaré coordinates for ${\mathrm{AdS}}_3$. We refer to these as global-CFT, Rindler-CFT and Poincaré-CFT, respectively. We demonstrate that the correlators for these CFTs are different and argue that the bulk duals to these should agree up to very close to the respective horizons but then start differing. Since the BTZ black hole is obtained as a quotient of ${\mathrm{AdS}}_3$, we discuss the implications of our results for bulk duals of periodically identified Poincaré and Rindler-CFTs. Our results are consistent with some recent proposals suggesting a modification of the semiclassical BTZ geometry close to the horizons.

We study how the coupling with gravity of theories with nonlinearly realized spacetime symmetries is modified when one changes the parametrization of the coset. As an example, we focus on the so-called Galileon duality: a reparametrization which maps a Galilean invariant action into another one which enjoys the same symmetry. Starting with a standard coupling with gravity, with a parametric separation between the Planck scale and the typical scale of the coset, one ends up with a theory without such a separation. In particular an infinite set of higher-dimension operators are relevant when the superluminality of the Galileon is measurable in the effective theory. This addresses an apparent paradox since superluminality arises in the dual theory even when absent in the original one.