We formulate a $N=(2,0)$ supersymmetric non-Abelian Proca-Stückelberg theory in six space-time dimensions (6D). As the foundation of our construction, we start with our recent work on $N=1$ supersymmetric Proca-Stückelberg formulation in 4D with a Yang-Mills (YM) multiplet $({A_{\mu }}^I,{\lambda }^I)$ and a chiral multiplet $({\phi }^I,{\chi }^I,{\varphi }^I)$, where the index $I=1,2,\dots ,\dim G$ is for the adjoint representation of a non-Abelian group $G$, while ${\phi }^I$ parametrizes the coordinates of the group manifold $G$. Since ${\phi }^I$ and ${\varphi }^I$ transform differently under $G$, the conventional global $R$ symmetry is lost. Next, we apply this mechanism to 6D with the two multiplets: a YM multiplet $({A_{\mu }}^I,{\lambda }^{\underset{\_}{\alpha }I})$ and a hypermultiplet (HM) $({\varphi }^{iJ},{{\chi }_{\underset{\_}{\alpha }}}^I,{\phi }^I)$. The index $i=1,2,3$ is for the $\mathbf{3}$ of $Sp(1)$. The spinorial index $\underset{\_}{\alpha }=(\alpha ,A)$ ($\alpha =1,\dots ,4$) is for the Majorana-Weyl spinor index for $D=5+1$ with $A=1,2$ for the $\mathbf{2}$ of $Sp(1)$. As opposed to the common notion that all four scalars in a HM in 6D must form the ($\mathbf{2},\mathbf{2}$) of global $Sp(1)\times Sp(1)$, we can use a scalar ${\phi }^I$ in the ($\mathbf{1},\mathbf{1}$) of $Sp(1)\times Sp(1)$ as a Nambu-Goldstone boson absorbed into the longitudinal component of ${A_{\mu }}^I$, separated from the remaining three scalars ${\varphi }^{iI}$ in the ($\mathbf{3},\mathbf{1}$) of $Sp(1)\times Sp(1)$. Similar to our recent result in 4D with broken automorphism $R$ symmetry, the new feature of our result is that all four scalars in the HM in 6D do not have to form the ($\mathbf{2},\mathbf{2}$) of $Sp(1)\times Sp(1)$.

We produce the first astrophysically relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detection, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasinormal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio $\gtrsim 180–240$, with the precise value depending on the dimension of the GR waveform family used in data analysis.

We derive a full analytical approximation to the stochastic gravitational wave background generated by the loops that are produced throughout the cosmological evolution of cosmic string networks. We show that this approximation not only predicts the amplitude of the radiation-era plateau exactly, but also provides a good fit to the high-frequency cutoff and to the low-frequency peak generated by the loops that decay during the matter era, irrespective of cosmic string tension and of the length of loops created. We then find that it provides a good quantitative description of the full stochastic gravitational wave background across the relevant frequency range.

A new model for tiny neutrino masses is proposed in the gauge theory of $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$, where neutrino masses are generated via the quantum effect of new particles. In this model, the fermion content is taken to be minimal to realize the gauge anomaly cancellation, while the scalar sector is extended from the minimal 3-3-1 model to have an additional $SU(3{)}_L$ triplet field. After $SU(3{)}_L\otimes U(1{)}_X$ is broken into $SU(2{)}_L\otimes U(1{)}_Y$, the “Zee model” like diagrams are naturally induced, which contain sufficient lepton flavor violating interactions to reproduce current neutrino oscillation data. Furthermore, the remnant $Z_2$ symmetry appears after the electroweak symmetry breaking, which guarantees the stability of dark matter. It is confirmed that this model can satisfy current dark matter data. As an important prediction to test this model, production and decays of doubly charged scalar bosons at collider experiments are discussed in successful benchmark scenarios.

We propose a new search for light scalar singlets in rare meson decays. For couplings well below the electroweak interaction strength, the scalar is long-lived at detector scales and decays into displaced pairs of leptons or light mesons. We show that Belle II has a remarkable potential to probe scalars in the GeV range with couplings as small as ${10}^{-5}$. The predicted sensitivity is higher than at the long-baseline experiments NA62 and FASER and comparable with projections for FASER 2. We also investigate signatures of invisibly decaying scalars in rare meson decays with missing energy.

Conventional hadron interpolating fields, which utilize gauge-covariant Gaussian smearing, are ineffective in isolating ground state nucleons in a uniform background magnetic field. There is evidence that residual Landau-mode physics remains at the quark level, even when QCD interactions are present. In this work, quark-level projection operators are constructed from the $\mathrm{SU}(3)\times \mathrm{U}(1)$ eigenmodes of the two-dimensional lattice Laplacian operator associated with Landau modes. These quark-level modes are formed from a periodic finite lattice where both the background field and strong interactions are present. Using these eigenmodes, quark-propagator projection operators provide the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarizability of both the proton and neutron is calculated using this method on the ${32}^3\times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. A chiral effective-field theory analysis is used to connect the lattice QCD results to the physical regime, obtaining magnetic polarizabilities of ${\beta }^p=2.79(22)({}_{-18}^{+13})\times {10}^{-4}{\mathrm{fm}}^3$ and ${\beta }^n=2.06(26)({}_{-20}^{+15})\times {10}^{-4}{\mathrm{fm}}^3$, where the numbers in parentheses describe statistical and systematic uncertainties.

In this work we present the isovector flavor combination for the nucleon tensor charge extracted from lattice QCD simulations using overlap fermions on $N_f=2+1$ domain-wall configurations. The pion mass dependence is studied using six valence quark masses, each reproducing a value for the pion mass in the valence sector between 147 and 330 MeV. We investigate and eliminate systematic uncertainties due to contamination by excited states, by employing several values for the source-sink separation that span from 1 to 1.6 fm. We apply a chiral extrapolation in the valence sector using a quadratic and a logarithmic term to fit the pion mass dependence, which describes well the lattice data. The lattice matrix element is renormalized nonperturbatively, and the final result is $g_T=1.096(30)$ in the $\overline{\mathrm{MS}}$ scheme at a renormalization scale of 2 GeV.

We investigate the hidden-charm pentaquarks as superpositions of ${\mathrm{\Lambda }}_c{\overline{D}}^{(*)}$ and ${\mathrm{\Sigma }}_c^{(*)}{\overline{D}}^{(*)}$ (isospin $I=1/2$) meson-baryon channels coupled to a $uudc\overline{c}$ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can consistently explain the masses and decay widths of $P_c^{+}(4312)$, $P_c^{+}(4440)$ and $P_c^{+}(4457)$ with the dominant components of ${\mathrm{\Sigma }}_c\overline{D}$ and ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ with spin-parity assignments $J^P=1/2^{-}$, $3/2^{-}$ and $1/2^{-}$, respectively. We analyze basic properties of the $P_c$’s such as masses and decay widths, and find that the mass ordering is dominantly determined by the quark dynamics while the decay widths by the tensor force of the one-pion exchange.

In this work, we present a study to probe the nature of interactions between black hole microstructures for the case of the Banados, Teitelboim, and Zanelli (BTZ) black holes. Even though BTZ black holes without any angular momentum or electric charge thermodynamically behave as an ideal gas, i.e., with noninteracting microstructures; in the presence of electric charge or angular momentum, BTZ black holes are associated with repulsive interactions among the microstructures. We extend the study to the case of exotic BTZ black holes with mass $M=\alpha m+\gamma \frac{j}{l}$ and angular momentum $J=\alpha j+\gamma lm$, for arbitrary values of $(\alpha ,\gamma )$ ranging from purely exotic $(\alpha =0,\gamma =1)$ to slightly exotic $(\alpha >\frac{1}{2},\gamma <\frac{1}{2})$ to highly exotic $(\alpha <\frac{1}{2},\gamma >\frac{1}{2})$. We find that, unlike the normal BTZ black holes [the case ($\alpha =1$, $\gamma =0$)], there exist both attraction as well as repulsion dominated regions in all the cases of exotic BTZ black holes.

From the partition function for two classes of classically nonlocal actions containing the fractional Laplacian, we show that as long as there exists a suitable (nonlocal) Hilbert-space transform the underlying action can be mapped onto a purely local theory. In all such cases the partition function is equivalent to that of a local theory and an area law for the entanglement entropy obtains. When such a reduction fails, the entanglement entropy deviates strongly from an area law and can in some cases scale as the volume. As these two criteria are coincident, we conjecture that they are equivalent and provide the ultimate test for locality of Gaussian theories rather than a simple inspection of the explicit operator content.

Extending the principle of local gauge invariance $\psi (x)\to \exp (𝚤{\sum }_A{\omega }^A(x)T^A)\psi (x),x\in {\mathbb{R}}^d$, with $T^A$ being the generators of the gauge group $\mathcal{A}$, to the fields $\psi (g)\equiv ⟨\chi |{\mathrm{\Omega }}^{*}(g)|\psi ⟩$, defined on a locally compact Lie group $G$, $g\in G$, where $\mathrm{\Omega }(g)$ is a suitable square-integrable representation of $G$, it is shown that taking the coordinates ($g$) on the affine group, we get a gauge theory that is finite by construction. The renormalization group in the constructed theory relates to each other the charges measured at different scales. The case of the $\mathcal{A}=SU(N)$ gauge group is considered.

Extending a previous work by the present authors, we investigate the existence of expansion-free dynamical stars with nonzero spatial twist and rotation and show that such stars cannot exist. First, it is shown that a rotating expansion-free dynamical star with zero twist cannot exist because such stars cannot radiate and are shear-free, in which case the energy density $\rho$ is time independent. Second, we prove that a nonrotating expansion-free dynamical star with nonzero spatial twist also cannot exist, as either the strong energy condition must be violated, i.e., $\rho +3p<0$, or the star must be shear-free, in which case the star is static ($\mathrm{\Theta }=\mathrm{\Omega }=\mathrm{\Sigma }=0$). Finally, if we insist that the rotation and spatial twist are simultaneously nonzero, then the star cannot be shear-free, in which case we obtain a quadratic polynomial equation in $\varphi$ and $\mathrm{\Sigma }$ with no real solutions. Therefore, such stars cannot exist.

The holographic interpretation of the Randall-Sundrum model based on the adaptation of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence to the braneworld scenario states that the black holes localized on the brane are quantum corrected. This can be better understood from the fact that the classical ${\mathrm{AdS}}_5$ bulk dynamics is dual to gravity coupled with conformal field theory (CFT) on the four-dimensional brane. Based on the backreaction of the CFT on the classical black hole geometry, localized on the brane, it is expected that there exist possible near-horizon modifications. This may result in the black hole horizon becoming partially reflective, thus giving rise to echoes in the ringdown signal in gravitational wave observations. In this paper, we investigate the existence of such echoes in the ringdown phase of a black hole localized on the brane, carrying a negative tidal charge, and establish the layout for future investigation of higher-dimensional effects in the ringdown signal. Confirmed detections of echoes at the current levels of instrumental sensitivity can constrain the dimensionless value of tidal charge to $|Q|\lesssim M^2$.

This paper is devoted to discussing compact stars in $f(\mathcal{R},\mathcal{G})$ gravity, where $\mathcal{R}$ and $\mathcal{G}$ denote the Ricci scalar and Gauss-Bonnet invariant, respectively. To meet this aim, we consider spherically symmetric space-time with an anisotropic fluid distribution. In particular, the Karmarkar condition is used to explore the compact star solutions. Furthermore, we choose two specific models of compact stars, namely LMC X-4 ($\mathrm{mass}=1.29M/M_{\odot }$ and $\mathrm{radii}=9.711\mathrm{km}$) and EXO 1785-248 ($\mathrm{mass}=1.30M/M_{\odot }$ and $\mathrm{radii}=8.849\mathrm{km}$). We develop the field equations for $f(\mathcal{R},\mathcal{G})$ gravity by employing the Karmarkar condition with a specific model already reported in literature by Lake [Phys. Rev. D 67, 104015 (2003)]. We further consider the Schwarzschild geometry for the matching conditions at the boundary. It is important to mention here that we calculate the values of all the involved parameters by imposing the matching condition. We have provided a detailed graphical analysis to discuss the physical acceptability of parameters, i.e., energy density, pressure, anisotropy, and gradients. We have also examined the stability of compacts stars by exploring the energy conditions, equation of state, generalized Tolman-Oppenheimer-Volkoff equation, causality condition, and adiabatic index. For the present analysis, we predict some numerical values in tabular form for central gravitational metric functions, central density, and central pressures components. We have also calculated the ratio $p_{rc}/{\rho }_c$ to check the validity of Zeldovich’s condition. Conclusively, it is found that our obtained solutions are physically viable with a well-behaved nature in $f(\mathcal{R},\mathcal{G})$ modified gravity for the compact star models under discussion.

We investigate the stable circular orbits of the spinning test particles around the accelerating Kerr black hole on the equatorial plane. To this end, we first calculate the equations of motion and analyze the parameter space for the particles. We study the effect of the particle’s spin and the black hole’s acceleration on the conserved angular momentum, conserved energy and radius of the spinning test particle on the innermost stable circular orbit. We find that the effect of the particle’s spin on the orbit parameters is almost linear, the effect of the black hole’s acceleration on those parameters is nonlinear. We also explore the effects of the particle’s spin and the black hole’s acceleration on the periastron shift for the spinning particle in the nearly stable circular orbit.

The parametrized post-Einsteinian formalism was developed to search for generic deviations from general relativity with gravitational waves. We here present constraints on this framework using Bayesian analysis of a set of binary pulsar observations. In particular, we use measurements of the Keplerian and post-Keplerian parameters of six different binary pulsar systems, and Markov-Chain Monte-Carlo exploration to calculate posteriors on the parametrized post-Einsteinian parameters and derive robust constraints. We find improvements of 1–2 orders of magnitude in the strength of constraints when combining all six observations, relative to what one can achieve when using only the double binary pulsar. We also find that the constraints are robust to any correlation with the binary’s component masses. The bounds on the parametrized post-Einsteinian framework derived here could be used as a prior in future Bayesian tests of general relativity with gravitational wave observations.

The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of general relativity à la Einstein attributes gravity to the spacetime curvature, to which we have grown accustomed. However, this perception has masked the fact that two alternative, though equivalent, formulations of general relativity in flat spacetimes exist, where gravity can be fully ascribed either to torsion or to nonmetricity. The latter allows a simpler geometrical formulation of general relativity that is oblivious to the affine spacetime structure. Generalizations along this line permit us to generate teleparallel and symmetric teleparallel theories of gravity with exceptional properties. In this work we explore modified gravity theories based on nonlinear extensions of the nonmetricity scalar. After presenting some general properties and briefly studying some interesting background cosmologies (including accelerating solutions with relevance for inflation and dark energy), we analyze the behavior of the cosmological perturbations. Tensor perturbations feature a rescaling of the corresponding Newton’s constant, while vector perturbations do not contribute in the absence of vector sources. In the scalar sector we find two additional propagating modes, hinting that $f(Q)$ theories introduce, at least, 2 additional degrees of freedom. These scalar modes disappear around maximally symmetric backgrounds because of the appearance of an accidental residual gauge symmetry corresponding to a restricted diffeomorphism. We finally discuss the potential strong coupling problems of these maximally symmetric backgrounds caused by the discontinuity in the number of propagating modes.

We study the details of eternal inflation in the presence of a spectator Higgs field within the framework of the minimal Standard Model. We have recently shown that in the presence of scalar field(s) which allow inflation only within a finite domain of field values, the Universe reaches a steady state where the normalized distribution for the field(s) converges to a steady state distribution [Phys. Rev. D 100, 023513 (2019)]. In this paper, we analyze this eternal inflation scenario with the renormalized Standard Model Higgs potential, since it also allows inflation in a finite domain, but turns over at high scales due to the running of the self-coupling, marking an exit from inflation. We compute the full steady state distribution for the Higgs using an integral evolution technique that we formulated in Phys. Rev. D 100, 023513 (2019) and the fractal dimension of the Universe. We then obtain a bound on the inflationary Hubble scale in order to have a large observable universe contained within the instability scale of $H\lesssim \mathcal{O}({10}^9)\mathrm{GeV}$ depending on the top mass. Upon reheating of the Universe, thermal fluctuations in the Higgs field could potentially pose another problem; however, we compute the rate of thermal bubble production and find that the probability of tunneling in the postinflationary era is negligibly small even for very high reheat temperatures.

In this work, we obtain measurements of the Hubble constant in the context of modified gravity theories. We set up our theoretical framework by considering viable cosmological $f(R)$ and $f(T)$ models, and we analyzed them through the use of geometrical datasets obtained in a model-independent way, namely, gravitationally lensed quasars with measured time delays, standard clocks from cosmic chronometers, and standard candles from the Pantheon Supernovae Ia sample. We find $H_0=(72.4\pm 1.4)\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ and $H_0=(71.5\pm 1.3)\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ for the $f(R)$ and $f(T)$ models, respectively. Our results represent 1.9% and 1.8% measurements of the Hubble constant, which are fully consistent with the local estimate of $H_0$ by the Hubble Space Telescope. We do not find significant departures from general relativity, as our study shows that the characteristic parameters of the extensions of gravity beyond general relativity are compatible with the $\mathrm{\Lambda }\mathrm{CDM}$ cosmology. Moreover, within the standard cosmological framework, our full joint analysis suggests that it is possible to measure the dark energy equation of state parameter at 1.2% accuracy, although we find no statistical evidence for deviations from the cosmological constant case.

Fuzzy dark matter (FDM) is one of the recent models for dark matter. According to this model, dark matter is made of very light scalar particles with considerable quantum mechanical effects on the galactic scale, which solves many problems of cold dark matter (CDM). Here we use the observed data from the rotation curve of the Milky Way (MW) Galaxy to compare the results from FDM and CDM models. We show that FDM adds a local peak on the rotation curve close to the center of the bulge, where its position and amplitude depend on the mass of FDM particles. By fitting the observed rotation curve with our expectation from FDM, we find that the mass of FDM is $m=2.5_{-2.0}^{+3.6}\times {10}^{-21}\mathrm{eV}$. We note that the local peak of the rotation curve in MW can also be explained in the CDM model with an extra inner bulge model for the MW Galaxy. We conclude that the FDM model explains this peak without a need for extra structure for the bulge.