We develop exceptional field theory for ${\mathrm{E}}_{8(8)}$, defined on a ($3+248$)-dimensional generalized spacetime with extended coordinates in the adjoint representation of ${\mathrm{E}}_{8(8)}$. The fields transform under ${\mathrm{E}}_{8(8)}$ generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an “internal” dreibein and an ${\mathrm{E}}_{8(8)}$-valued “zweihundertachtundvierzigbein” (248-bein). Crucially, the theory also features gauge vectors for the ${\mathrm{E}}_{8(8)}$ E bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained ${\mathrm{E}}_{8(8)}$ gauge symmetry. The complete bosonic theory, with a novel Chern-Simons term for the gauge vectors, is uniquely determined by gauge invariance under internal and external generalized diffeomorphisms. The theory consistently comprises components of the dual graviton encoded in the 248-bein. Upon picking particular solutions of the constraints the theory reduces to $D=11$ or type IIB supergravity, for which the dual graviton becomes pure gauge. This resolves the dual graviton problem, as we discuss in detail.

We review the extended mean field theory (EMFT) approximation and apply it to complex, scalar ${\phi }^4$ theory on the lattice. We study the critical properties of the Bose condensation driven by a nonzero chemical potential $\mu$ at both zero and nonzero temperature and determine the $(T,\mu )$ phase diagram. The results are in very good agreement with recent Monte Carlo data for all parameter values considered. EMFT can be formulated directly in the thermodynamic limit which allows us to study lattice spacings for which Monte Carlo studies are not feasible with present techniques. We find that the EMFT approximation accurately reproduces many known phenomena of the exact solution, like the “Silver Blaze” behavior at zero temperature and dimensional reduction at finite temperature.

We have performed a complete study of BPS vortex solutions in the Abelian sector of the standard model extension (SME). Specifically, we have coupled the SME electromagnetism with a Higgs field which is supplemented with a Lorentz-violating CPT-even term. We have verified that Lorentz violation (LV) belonging to the Higgs sector allows us to interpolate between some well-known models like Maxwell-Higgs, Chern-Simons-Higgs, and Maxwell-Chern-Simons-Higgs. We can also observe that the electrical charged density distribution is non-null in both CPT-even and CPT-odd models; however, the total electric charge in the CPT-even case is null, whereas in the CPT-odd one it is proportional to the quantized magnetic flux. The following general results can be established in relation to the LV introduced in the Higgs sector: it changes the vortex ansatz and the gauge field boundary conditions. A direct consequence is that the magnetic flux, besides being proportional to the winding number, also depends explicitly on the Lorentz-violation belonging to the Higgs sector.

Using a component formulation, we construct the supersymmetric action for a superparticle in a three-dimensional Newton–Cartan supergravity background and clarify its symmetries. Our construction proceeds by first constructing the superparticle in a flat background. Next, by boosting up the background symmetries, we replace in a first step the flat background by a Galilean supergravity background. In a second step the Galilean supergravity background is replaced by a Newton–Cartan supergravity background. We extend our results by adding a supersymmetric cosmological constant and compare the nonrelativistic superparticle with the relativistic $\kappa$-symmetric three-dimensional superparticle.

Based on the features of chiral susceptibility and thermal susceptibility at finite temperature, the nature of chiral phase transition around the critical number of fermion flavors ($N_c$) and the critical temperature ($T_c$) at a fixed fermion flavors number in massless ${\mathrm{QED}}_3$ is investigated. It is showed that, at finite temperature, the system exhibits a second-order phase transition at $N_c$ or $T_c$ and each of the estimated critical exponents is less than 1, while it reveals a higher-order continuous phase transition around $N_c$ at zero temperature.

Recently, in the context of dS/CFT correspondence, quasinormal modes have been put forward to address certain features of this conjecture. In particular, it is argued that the dual states of quasinormal modes are in fact the states of ${\mathrm{CFT}}_3$ which are created by operator insertions. For a scalar field in ${\mathrm{dS}}_4$, quasinormal modes which are singular on the past horizon of the south pole and decay exponentially towards the future have been considered in [G. S. Ng and A. Strominger, Classical Quantum Gravity 30, 104002 (2013); D. L. Jafferis et al., arXiv:1305.5523]; these modes lie in two complex highest-weight representations of the ${\mathrm{dS}}_4$ isometry group. In this work, we present a simple group representation analysis of these modes so that the de Sitter invariance is obviously manifest. By making use of the so-called plane wave method, we will show that the quasinormal modes correspond to one class of the unitary irreducible representation of the de Sitter group. This consideration could be generalized straightforwardly for higher-spin fields and higher dimensions; in particular, we will study the quasinormal modes for gauge and spinor fields, and, in the case of a scalar field, the generalization to higher dimensions is also obtained.

The Einstein Telescope, a proposed third-generation gravitational-wave observatory, would enable tests of the no-hair theorem by looking at the characteristic frequencies and damping times of black hole ringdown signals. In previous work it was shown that with a single $500–1000M_{\odot }$ black hole at a distance $\lesssim 6$ Gpc (or redshift $z\lesssim 1$), deviations of a few percent in the frequencies and damping times of dominant and subdominant modes would be within the range of detectability. Given that such sources may be relatively rare, it is of interest to see how well the no-hair theorem can be tested with events at much larger distances and with smaller signal-to-noise ratios, thus accessing a far bigger volume of space and a larger number of sources. We employ a model-selection scheme called TIGER (Test Infrastructure for GEneral Relativity), which was originally developed to test general relativity with weak binary coalescence signals that will be seen in second-generation detectors, such as Advanced LIGO and Advanced Virgo. TIGER is well suited for the regime of low signal-to-noise ratios, and information from a population of sources can be combined so as to arrive at a stronger test. By performing a range of simulations using the expected noise power spectral density of the Einstein Telescope, we show that with TIGER, similar deviations from the no-hair theorem (such as those considered in previous works) will be detectable with great confidence using $\mathcal{O}(10)$ sources distributed uniformly in a comoving volume out to $50\mathrm{Gpc}(z\lesssim 5)$.

The resultant response of the rotating torsion-bar antenna for gravitational waves discussed in M. Ando et al. [Phys. Rev. Lett. 105, 161101 (2010)] is reinvestigated from a general-relativistic point of view. To do this, the equation of motion of a free-falling particle in the proper reference frame of a rotating observer is used. As a result, the resultant response derived in the above paper is also valid even when ${\omega }_g\sim \mathrm{\Omega }$, where ${\omega }_g$ and $\mathrm{\Omega }$ are the angular frequencies of gravitational waves and the rotation of the antenna, respectively.

The recently proposed model of “solid inflation” features a peculiar three-point function for scalar perturbations with an anisotropic, purely quadrupolar, squeezed limit. We confirm this result as well as the overall amplitude of the three-point function via an extremely simple computation, where we focus on the squeezed limit from the start and follow the standard logic adopted in deriving the consistency relations. Our system violates the consistency relations, but in the squeezed limit the three-point function can still be traded for a background-dependent two-point function, which is immediate to compute. Additionally, we use these simple methods to derive some new results—namely, certain squeezed limits of the three-point correlators involving vector and tensor perturbations as well.

Particle collisions in black hole ergoregions may result in extremely high center-of-mass energies that could probe new physics if escape to infinity were possible. Here we show that some geodesics at high inclinations to the equatorial plane may be unbound. Hence a finite flux of annihilation debris is able to escape, especially in the case of near-extremal Kerr black holes and if the Penrose process plays a role. For a class of Penrose processes, we show that the Wald inequalities are satisfied, allowing the Penrose process to have a key role in high-energy ejection. Hence the possibility of observing new physics effects from a black hole accelerator at unprecedentedly high particle collision energies remains a tantalizing, if futuristic, experimental vision.

The equation of state plays a critical role in the physics of the merger of two neutron stars. Recent numerical simulations with a microphysical equation of state suggest the outcome of such events depends on the mass of the neutron stars. For less massive systems, simulations favor the formation of a hypermassive, quasistable neutron star, for which the oscillations produce a short, high-frequency burst of gravitational radiation. Its dominant frequency content is tightly correlated with the radius of the neutron star, and its measurement can be used to constrain the supranuclear equation of state. In contrast, the merger of higher mass systems results in prompt gravitational collapse to a black hole. We have developed an algorithm that combines waveform reconstruction from a morphology-independent search for gravitational wave transients with the Bayesian model selection to discriminate between postmerger scenarios and accurately measure the dominant oscillation frequency. We demonstrate the efficacy of the method using a catalog of simulated binary merger signals in data from LIGO and Virgo, and we discuss the prospects for this analysis in advanced ground-based gravitational wave detectors. From the waveforms considered in this work, we find that the postmerger neutron star signal may be detectable by this technique to $\sim 4–12\mathrm{Mpc}$, for sources with random sky locations and orientations with respect to the Earth. We also find that we successfully discriminate between the postmerger scenarios with $\sim 95\%$ accuracy and determine the dominant oscillation frequency of surviving postmerger neutron stars to within $\sim 10\mathrm{Hz}$, averaged over all detected signals. This leads to an uncertainty in the estimated radius of a nonrotating $1.6M_{\odot }$ reference neutron star of $\sim 100\mathrm{m}$.

The gravitational lensing effect is important to the detection of electromagnetic signals in astrophysics. The gravitational wave lensing effect has also been found significant to gravitational wave detection in the past decade. Recent analysis shows that the lensing events for advanced detectors could be quite plausible. The black holes in our Milky Way Galaxy may play the role of lens objects. These facts motivate us to study the lensing effects on gravitational wave signals for advanced detectors. Taking advanced LIGO and Einstein Telescope for examples, we investigate the lensing effects on the parameter extraction of gravitational wave signals. Using the Markov chain Monte Carlo simulation together with matched filtering methods, we find that the lensing effect for a lens object with small mass is negligible. But when the mass of the lens object increases to larger than $1000M_{\odot }$ the lensing effect becomes important. Using the template without lensing corrections would result in loss of signal detections. In contrast if we consider templates with lensing effects, the lensed signal may provide much information about the lens black hole. These facts may give us a new way to determine the parameters of the lensing object. For example, this kind of signal may also help us estimate the mass and the distance of the supermassive black hole hosted at the center of our Galaxy.

Gravitational wave detectors are typically described as responding to gravitational wave metric perturbations, which are gauge-dependent and—correspondingly—unphysical quantities. This is particularly true for ground-based interferometric detectors, like LIGO, space-based detectors, like LISA and its derivatives, spacecraft Doppler tracking detectors, and pulsar timing array detectors. The description of gravitational waves, and a gravitational wave detector’s response, to the unphysical metric perturbation has lead to a proliferation of false analogies and descriptions regarding how these detectors function, and true misunderstandings of the physical character of gravitational waves. Here we provide a fully physical and gauge-invariant description of the response of a wide class of gravitational wave detectors in terms of the Riemann curvature, the physical quantity that describes gravitational phenomena in general relativity. In the limit of high frequency gravitational waves, the Riemann curvature separates into two independent gauge-invariant quantities: a “background” curvature contribution and a “wave” curvature contribution. In this limit the gravitational wave contribution to the detector response reduces to an integral of the gravitational wave contribution of the curvature along the unperturbed photon path between components of the detector. The description presented here provides an unambiguous physical description of what a gravitational wave detector measures and how it operates, a simple means of computing corrections to a detectors response owing to general detector motion, a straightforward way of connecting the results of numerical relativity simulations to gravitational wave detection, and a basis for a general and fully relativistic pulsar timing formula.

We present a method to directly solve the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators, and the Bethe-Salpeter amplitude itself. The off-mass-shell scattering amplitude for spinless particles interacting by a one-boson exchange is computed for the first time.

We give a quantitative analysis of the electric dipole moments as a probe of high scale physics. We focus on the electric dipole moment of the electron since the limit on it is the most stringent. Further, theoretical computations of it are free of QCD uncertainties. The analysis presented here first explores the probe of high scales via electron electric dipole moment (EDM) within minimal supersymmetric standard model where the contributions to the EDM arise from the chargino and the neutralino exchanges in loops. Here it is shown that the electron EDM can probe mass scales from tens of TeV into the PeV range. The analysis is then extended to include a vectorlike generation which can mix with the three ordinary generations. Here new $CP$ phases arise and it is shown that the electron EDM now has not only a supersymmetric (SUSY) contribution from the exchange of charginos and neutralinos but also a nonsupersymmetric contribution from the exchange of $W$ and $Z$ bosons. It is further shown that the interference of the supersymmetric and the nonsupersymmetric contribution leads to the remarkable phenomenon where the electron EDM as a function of the slepton mass first falls and become vanishingly small and then rises again as the slepton mass increases. This phenomenon arises as a consequence of cancellation between the SUSY and the non-SUSY contribution at low scales while at high scales the SUSY contribution dies out and the EDM is controlled by the non-SUSY contribution alone. The high mass scales that can be probed by the EDM are far in excess of what accelerators will be able to probe. The sensitivity of the EDM to $CP$ phases both in the SUSY and the non-SUSY sectors are also discussed.

The ATLAS and CMS Collaborations have observed independently at the LHC a new Higgs-like particle with a mass $M_h\sim 125\mathrm{GeV}$ and properties similar to that predicted by the Standard Model (SM). Although the measurements indicate that this Higgs-like boson is compatible with the SM hypothesis, due to large uncertainties in some of the Higgs detection channels, one still has the possibility of testing this object as being a candidate for some beyond the SM physics scenarios, for example, the minimal supersymmetric Standard Model (MSSM), in the $CP$-conserving version (CPC-MSSM). In this paper, we evaluate the modifications of these CPC-MSSM results when $CP$-violating (CPV) phases are turned on explicitly, leading to the $CP$-violating MSSM (CPV-MSSM). We investigate the effect of the CPV phases in (some of) the soft supersymmetry (SUSY) terms on both the mass of the lightest Higgs boson $h_1$, and the rates for the processes $gg\to h_1\to \gamma \gamma$, $gg\to h_1\to Z{Z}^{*}\to 4l$, $gg\to h_1\to W{W}^{*}\to l\nu l\nu$, $pp\to V{h}_1\to Vb\overline{b}$ and $pp\to V{h}_1\to V{\tau }^{+}{\tau }^{-}$, ($V\equiv W^{\pm },Z$) at the LHC, considering the impact of the flavor constraints as well as the constraints coming from the electric dipole moment measurements. We find that it is possible to have a Higgs mass of about 125 GeV with relatively small $\tan \beta$, large $A_t$ and a light top squark, which is consistent with the current SUSY particle searches at the LHC. We obtain that the imaginary part of the top and bottom Yukawa couplings can take very small but nonzero values even after satisfying the recent updates from both the ATLAS and CMS Collaborations within $1–2\sigma$ uncertainties which might be an interesting signature to look for at the future run of the LHC. Our study shows that the CPV-MSSM provides an equally possible solution (like its $CP$-conserving counterpart) to the recent LHC Higgs data, in fact offering very little in the way of distinction between these two SUSY models (CPC-MSSM and CPV-MSSM) at the 7 and 8 TeV runs of the LHC. Improvement in different Higgs coupling measurements is necessary in order to test the possibility of probing the small dependence on these CPV phases in the Higgs sector of the MSSM.

We propose a class of the two Higgs doublet standard models (SMs) with a SM singlet and a class of supersymmetric SMs with two pairs of Higgs doublets, where the right-handed up/charm quarks and the right-handed top quark have different quantum numbers under extra discrete symmetries. Thus, the right-handed up and charm quarks couple to one Higgs doublet field, while the right-handed top quark couples to another Higgs doublet. The quark Cabibbo-Kobayashi-Maskawa mixings can be generated from the down-type quark sector. As one of the phenomenological consequences of our models, we explore whether one can accommodate the observed direct $CP$ asymmetry difference in singly Cabibbo-suppressed D decays. We how that it is possible to explain the measured values of $CP$ violation under relevant experimental constraints.

Now that lattice QCD calculations are beginning to include QED, it is important to better understand how hadronic properties are modified by finite-volume QED effects. They are known to exhibit power-law scaling with volume, in contrast to the exponential behavior of finite-volume strong interaction effects. We use nonrelativistic effective field theories describing the low-momentum behavior of hadrons to determine the finite-volume QED corrections to the masses of mesons, baryons and nuclei out to $\mathcal{O}(1/{\mathrm{L}}^4)$ in a volume expansion, where L is the spatial extent of the cubic volume. This generalizes the previously determined expansion for mesons, and extends it by two orders in $1/\mathrm{L}$ to include contributions from the charge radius, magnetic moment and polarizabilities of the hadron. We make an observation about direct calculations of the muon $g-2$ in a finite volume.

To validate the molecular description of the observed $Z_b(10610)/Z_b(10650)$ and $Z_c(3900)/Z_c(4025)$, it is valuable to investigate their counterparts, denoted as $Z_{QV}^{(\prime )}$ in this work, and the corresponding decay modes. In this work, we present an analysis of the $Z_{QV}^{(\prime )}$ using flavor symmetry. We also use the effective Lagrangian based on the heavy quark symmetry to explore the rescattering mechanism and calculate the partial widths for the isospin conserved channels $Z_{QV}^{(\prime )}\to {\eta }_{Q}V$. The predicted partial widths are of an order of MeV for $Z_{QV}\to {\eta }_{Q}V$ which corresponds to branching ratios of the order ${10}^{-2}\sim {10}^{-1}$. For $Z_{QV}^{\prime }\to {\eta }_{Q}V$, the partial widths are a few hundreds of keV and the branching ratios are about $10^{-3}$. Future experimental measurements can test our predictions on the partial widths and thus examine the molecule description of heavy quarkoniumlike exotic states.