The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using the exact renormalization group equations has been studied, motivated by the recently found nontrivial fixed point in $4<d<6$ dimensions with metastable critical potential. Particular attention is paid to the case of $d=5$ where the scaling exponent $\nu$ has the value $1/3$, which coincides with the scaling exponent of quantum gravity in one fewer dimensions. Convincing results show that this relation could be generalized to arbitrary number of dimensions above five. Some aspects of AdS/CFT correspondence are also discussed.

The topological terms of the bulk effective action for the integer quantum Hall effect, capturing the dynamics of gauge and gravitational fluctuations, reveal a curiosity, namely, the Abelian potential for the magnetic field appears in a particular combination with the Abelian spin connection. This seems to hold for the quantum Hall effect on complex projective spaces of arbitrary dimensions. An interpretation of this in terms of the algebra of symplectic transformations is given. This can also be viewed in terms of the metaplectic correction in geometric quantization.

We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator $N$ is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which $N$ grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.

We show that complex, massive spin-1 fields minimally coupled to Einstein’s gravity with a negative cosmological constant, admit asymptotically anti–de Sitter self-gravitating solutions. Focusing on four-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti–de Sitter background, and then find fully nonlinear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in five dimensions.

We study the stability of the Vainshtein screening solution of massive gravity/bigravity based on the massive nonlinear sigma model as the effective action inside the Vainshtein radius. The effective action is obtained by taking the ${\mathrm{\Lambda }}_2$ decoupling limit around a curved spacetime. First we derive a general consequence that any Ricci flat Vainshtein screening solution is unstable when we take into account the excitation of the scalar graviton only. This instability suggests that the nonlinear excitation of the scalar graviton is not sufficient to obtain a successful Vainshtein screening in massive gravity/bigravity. Then to see the role of the excitation of the vector graviton, we study perturbations around the static and spherically symmetric solution obtained in bigravity explicitly. As a result, we find that linear excitations of the vector graviton cannot be helpful and the solution still suffers from a ghost and/or a gradient instability for any parameters of the theory for this background.

We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact solution for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a $1+1$-dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal. The scattering coefficients were previously obtained by Busch and Parentani in a study of dispersive fields in de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further details of the wave propagation in this exactly solvable case, where our focus is on laboratory systems.

In this paper we investigate the non-Abelian cosmic string in de Sitter and anti–de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also of the metric tensor for specific values of the physical parameters of the theory. For the de Sitter case, we find the appearance of an horizon. This horizon is consequence of the presence of the cosmological constant, and its position strongly depends on the value of the gravitational coupling. In the anti–de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (00) and $(zz)$ components of the metric tensor. They present a strong increasing behavior for large distance from the string.

The second-order vector mode is inevitably induced from the coupling of first-order scalar modes in cosmological perturbation theory and might hinder a possible detection of primordial gravitational waves from inflation through 21 cm lensing observations. Here, we investigate the weak lensing signal in 21 cm photons emitted by neutral hydrogen atoms in the dark ages induced by the second-order vector mode by decomposing the deflection angle of the 21 cm lensing signal into the gradient and curl modes. The curl mode is a good tracer of the cosmological vector and tensor modes since the scalar mode does not induce the curl one. By comparing angular power spectra of the 21 cm lensing curl mode induced by the second-order vector mode and primordial gravitational waves whose amplitude is parametrized by the tensor-to-scalar ratio $r$, we find that the 21 cm curl mode from the second-order vector mode dominates over that from primordial gravitational waves on almost all scales if $r\lesssim {10}^{-5}$. If we use the multipoles of the power spectrum up to ${\ell }_{\max }=10^5$ and $10^6$ in reconstructing the curl mode from 21 cm temperature maps, the signal-to-noise ratios of the 21 cm curl mode from the second-order vector mode achieve $\mathrm{S}/\mathrm{N}\approx 0.46$ and 73, respectively. Observation of 21 cm radiation is, in principle, a powerful tool to explore not only the tensor mode but also the cosmological vector mode.

We derive constraints on dark matter (DM) annihilation cross section and decay lifetime from cross-correlation analyses of the data from Fermi-LAT and weak lensing surveys that cover a wide area of $\sim 660$ squared degrees in total. We improve upon our previous analyses by using an updated extragalactic $\gamma$-ray background data reprocessed with the Fermi Pass 8 pipeline, and by using well-calibrated shape measurements of about twelve million galaxies in the Canada-France-Hawaii Lensing Survey (CFHTLenS) and Red-Cluster-Sequence Lensing Survey (RCSLenS). We generate a large set of full-sky mock catalogs from cosmological $N$-body simulations and use them to estimate statistical errors accurately. The measured cross-correlation is consistent with null detection, which is then used to place strong cosmological constraints on annihilating and decaying DM. For leptophilic DM, the constraints are improved by a factor of $\sim 100$ in the mass range of $O(1)\mathrm{TeV}$ when including contributions from secondary $\gamma$ rays due to the inverse-Compton upscattering of background photons. Annihilation cross sections of $⟨\sigma v⟩\sim {10}^{-23}{\mathrm{cm}}^3/\mathrm{s}$ are excluded for TeV-scale DM depending on channel. Lifetimes of $\sim 10^{25}\sec$ are also excluded for the decaying TeV-scale DM. Finally, we apply this analysis to wino DM and exclude the wino mass around 200 GeV. These constraints will be further tightened, and all the interesting wino DM parameter region can be tested, by using data from future wide-field cosmology surveys.

$CP$-odd invariants provide a basis independent way of studying the $CP$ properties of Lagrangians. We propose powerful methods for constructing basis invariants and determining whether they are $CP$ odd or $CP$ even, then systematically construct all of the simplest $CP$-odd invariants up to a given order, finding many new ones. The $CP$-odd invariants are valid for general potentials when expressed in a standard form. We then apply our results to scalar potentials involving three (or six) Higgs fields which form irreducible triplets under a discrete symmetry, including invariants for both explicit as well as spontaneous $CP$ violation. The considered cases include one triplet of Standard Model (SM) gauge singlet scalars, one triplet of SM Higgs doublets, two triplets of SM singlets, and two triplets of SM Higgs doublets. For each case, we study the potential symmetric under one of the simplest discrete symmetries with irreducible triplet representations, namely $A_4$, $S_4$, $\mathrm{\Delta }(27)$ or $\mathrm{\Delta }(54)$, as well as the infinite classes of discrete symmetries $\mathrm{\Delta }(3n^2)$ or $\mathrm{\Delta }(6n^2)$.

The perturbative effective potential suffers infrared (IR) divergences in gauges with massless Goldstones in their minima (like the Landau or Fermi gauges), but the problem can be fixed by a suitable resummation of the Goldstone propagators. When the potential minimum is generated radiatively, gauge independence of the potential at the minimum also requires resummation, and we demonstrate that the resummation that solves the IR problem also cures the gauge-dependence issue, showing this explicitly in the Abelian Higgs model in the Fermi gauge. In the process, we find an IR divergence (in the first derivative of the potential) specific to the Fermi gauge and not appreciated in the recent literature. We show that physical observables can still be computed in this gauge, and we further show how to get rid of this divergence by a field redefinition. All these results generalize to the Standard Model case.

We suggest that the $J/\psi \varphi$ structures observed by LHCb can be fitted in two tetraquak multiplets, the $S$-wave ground state and the first radial excitation, with composition $[cs][\overline{c}\overline{s}]$. When compared to the previously identified $[cq][\overline{c}\overline{q}]$ multiplet, the observed masses agree with that expected for a multiplet with $q\to s$. We propose the $X(4274)$, fitted by LHCb with a single $1^{++}$ resonance, to correspond rather to two, almost degenerate, unresolved lines with $J^{PC}=0^{++},2^{++}$. Masses of missing particles in the $1S$ and $2S$ multiplets are predicted.

Properties of bottom and bottom-strange mesons are computed in two relativized quark models. Model masses and wave functions are used to predict radiative transition rates, and the ${}^3{P}_0$ quark pair creation model is used to compute strong decay widths. A comparison to recently observed bottom and bottom-strange states is made. We find that there are numerous excited $B$ and $B_s$ mesons that have relatively narrow widths and significant branching ratios to simple final states such as $B\pi$, $B^{*}\pi$, $BK$, and $B^{*}K$ that could be observed in the near future.

The pentaquark $P_c^{+}(4450)$ recently discovered by the LHCb has been interpreted as a bound state of $\mathrm{\Psi }(2S)$ and a nucleon. The charmonium-nucleon interaction which provides the binding mechanism is given, in the heavy-quark limit, in terms of charmonium chromoelectric polarizabilities and densities of the nucleon energy-momentum tensor. In this work, we show in a model-independent way, by exploring general properties of the effective interaction, that $\mathrm{\Psi }(2S)$ can form bound states with a nucleon and $\mathrm{\Delta }$. Using the Skyrme model to evaluate the effective interaction in the large-$N_c$ limit and estimate $1/N_c$ corrections, we confirm the results from prior work which were based on a different effective model (chiral quark soliton model). This shows that the interpretation of $P_c^{+}(4450)$ is remarkably robust and weakly dependent on the details of the effective theories for the nucleon energy-momentum tensor. We explore the formalism further and present robust predictions of isospin-$\frac{3}{2}$ bound states of $\mathrm{\Psi }(2S)$ and $\mathrm{\Delta }$ with masses around 4.5 GeV and widths around 70 MeV. The approach also predicts broader resonances in the $\mathrm{\Psi }(2S)\text{−}\mathrm{\Delta }$ channel at 4.9 GeV with widths of the order of 150 MeV. We discuss in which reactions these new isospin-$\frac{3}{2}$ pentaquarks with hidden charm can be observed.

Tensor-polarized parton distribution functions are new quantities in spin-1 hadrons such as the deuteron, and they could probe new quark-gluon dynamics in hadron and nuclear physics. In charged-lepton deep inelastic scattering, they are studied by the twist-2 structure functions $b_1$ and $b_2$. The HERMES Collaboration found unexpectedly large $b_1$ values compared to a naive theoretical expectation based on the standard deuteron model. The situation should be significantly improved in the near future by an approved experiment to measure $b_1$ at Thomas Jefferson National Accelerator Facility (JLab). There is also an interesting indication in the HERMES result that finite antiquark tensor polarization exists. It could play an important role in solving a mechanism on tensor structure in the quark-gluon level. The tensor-polarized antiquark distributions are not easily determined from the charged-lepton deep inelastic scattering; however, they can be measured in a proton-deuteron Drell-Yan process with a tensor-polarized deuteron target. In this article, we estimate the tensor-polarization asymmetry for a possible Fermilab Main-Injector experiment by using optimum tensor-polarized parton distribution functions to explain the HERMES measurement. We find that the asymmetry is typically a few percent. If it is measured, it could probe new hadron physics, and such studies could create an interesting field of high-energy spin physics. In addition, we find that a significant tensor-polarized gluon distribution should exist due to $Q^2$ evolution, even if it were zero at a low $Q^2$ scale. The tensor-polarized gluon distribution has never been observed, so it is an interesting future project.

The Schwinger mechanism of electron-positron pair production in the presence of strong external electric fields is analyzed numerically for the case of one- and two-dimensional field configurations where the external field depends both on time and one spatial coordinate. In order to provide this analysis, a new efficient numerical approach is developed. The number of particles created is obtained numerically and also compared with the analytical results for several exactly solvable one-dimensional backgrounds. For the case of two-dimensional field configurations the effects of the spatial finiteness are examined, which confirms their importance and helps us to attest our approach further. The corresponding calculations are also performed for several more interesting and nontrivial combinations of temporal and spatial inhomogeneities. Finally, we discuss the case of a spatially periodic external field when the approach is particularly productive. The method employed is described in detail.

We address the subject of chiral anomalies in two- and four-dimensional theories. Ambiguities associated with the ${\gamma }_5$ algebra within divergent integrals are identified, even though the physical dimension is not altered in the process of regularization. We present a minimal prescription that leads to unique results and apply it to a series of examples. For the particular case of Abelian theories with effective chiral vertices, we show (i) its implication on the way to display the anomalies democratically in the Ward identities, (ii) the possibility to fix an arbitrary surface term in such a way that a momentum routing independent result emerges—this leads to a reinterpretation of the role of momentum routing in the process of choosing the Ward identity to be satisfied in an anomalous process—and (iii) momentum routing invariance is a necessary and sufficient condition to assure vectorial gauge invariance of effective chiral Abelian gauge theories. We also briefly discuss the case of complete chiral theories, using the chiral Schwinger model as an example.

Modified gravity theories are a popular alternative to dark energy as a possible explanation for the observed accelerating cosmic expansion, and their cosmological tests are currently an active research field. Studies in recent years have been increasingly focused on testing these theories in the nonlinear regime, which is computationally demanding. Here we show that, under certain circumstances, a whole class of theories can be ruled out by using background cosmology alone. This is possible because certain classes of models (i) are fundamentally incapable of producing specific background expansion histories, and (ii) said histories are incompatible with local gravity tests. As an example, we demonstrate that a popular class of models, $f(R)$ gravity, would not be viable if observations suggest even a slight deviation of the background expansion history from that of the $\mathrm{\Lambda }\mathrm{CDM}$ paradigm.