Global conformal invariance determines the form of two- and three-point functions of quasiprimary operators in a conformal field theory and generates nontrivial relations between terms in the operator product expansion. These ideas are generalized to the principal and complementary series representations, which play an important role in the conjectured dS/CFT correspondence. The conformal partial wave expansions are constructed for these representations, which in turn determine the operator product expansion. This leads us to conclude that conformal field theories containing such representations have essential singularities, so they cannot be realized as conventional field theories.

We derive a closed expression for the vacuum expectation value (VEV) of the fermionic current density in a ($D+1$)-dimensional locally AdS spacetime with an arbitrary number of toroidally compactified Poincaré spatial dimensions and in the presence of a constant gauge field. The latter can be formally interpreted in terms of a magnetic flux treading the compact dimensions. In the compact subspace, the field operator obeys quasiperiodicity conditions with arbitrary phases. The VEV of the charge density is zero and the current density has nonzero components along the compact dimensions only. They are periodic functions of the magnetic flux with the period equal to the flux quantum and tend to zero on the AdS boundary. Near the horizon, the effect of the background gravitational field is small and the leading term in the corresponding asymptotic expansion coincides with the VEV for a massless field in the locally Minkowski bulk. Unlike the Minkowskian case, in the system consisting of an equal number of fermionic and scalar degrees of freedom, with same masses, charges and phases in the periodicity conditions, the total current density does not vanish. In these systems, the leading divergences in the scalar and fermionic contributions on the horizon are canceled and, as a consequence of that, the charge flux, integrated over the coordinate perpendicular to the AdS boundary, becomes finite. We show that in odd spacetime dimensions the fermionic fields realizing two inequivalent representations of the Clifford algebra and having equal phases in the periodicity conditions give the same contribution to the VEV of the current density. Combining the contributions from these fields, the current density in odd-dimensional $C$-,$P$- and $T$-symmetric models are obtained. As an application, we consider the ground state current density in curved carbon nanotubes described in terms of a ($2+1$)-dimensional effective Dirac model.

Hamiltonian truncation (also known as “truncated spectrum approach”) is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy “tail states.” We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.

Ultralight bosons can induce superradiant instabilities in spinning black holes, tapping their rotational energy to trigger the growth of a bosonic condensate. Possible observational imprints of these boson clouds include (i) direct detection of the nearly monochromatic (resolvable or stochastic) gravitational waves emitted by the condensate, and (ii) statistically significant evidence for the formation of “holes” at large spins in the spin versus mass plane (sometimes also referred to as “Regge plane”) of astrophysical black holes. In this work, we focus on the prospects of LISA and LIGO detecting or constraining scalars with mass in the range $m_s\in [{10}^{-19},{10}^{-15}]\mathrm{eV}$ and $m_s\in [{10}^{-14},{10}^{-11}]\mathrm{eV}$, respectively. Using astrophysical models of black-hole populations calibrated to observations and black-hole perturbation theory calculations of the gravitational emission, we find that, in optimistic scenarios, LIGO could observe a stochastic background of gravitational radiation in the range $m_s\in [2\times {10}^{-13},{10}^{-12}]\mathrm{eV}$, and up to $10^4$ resolvable events in a 4-year search if $m_s\sim 3\times {10}^{-13}\mathrm{eV}$. LISA could observe a stochastic background for boson masses in the range $m_s\in [5\times {10}^{-19},5\times {10}^{-16}]$, and up to $\sim {10}^3$ resolvable events in a 4-year search if $m_s\sim {10}^{-17}\mathrm{eV}$. LISA could further measure spins for black-hole binaries with component masses in the range $[{10}^3,{10}^7]M_{\odot }$, which is not probed by traditional spin-measurement techniques. A statistical analysis of the spin distribution of these binaries could either rule out scalar fields in the mass range $\sim [4\times {10}^{-18},{10}^{-14}]\mathrm{eV}$, or measure $m_s$ with ten percent accuracy if light scalars in the mass range $\sim [{10}^{-17},{10}^{-13}]\mathrm{eV}$ exist.

We derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First, we decompose the manifold via a $1+1+2$ semitetrad formalism that yields a set of geometrical and thermodynamic scalars for the spacetime. We then recast the Einstein field equations in terms of evolution and propagation of these scalars. It is then shown that this class of spacetimes must possess self-similarity and we use this property to solve for these scalars, thus obtaining a general solution. This solution has a number of very interesting cosmological or astrophysical consequences which we discuss in detail.

In $\mu$-hybrid inflation a nonzero inflaton vacuum expectation value induced by supersymmetry breaking is proportional to the gravitino mass $m_{3/2}$, which can be exploited to resolve the minimal supersymmetric standard model $\mu$ problem. We show how this scenario can be successfully implemented with $m_{3/2}\sim 1–100\mathrm{TeV}$ and reheat temperature as low as $10^6\mathrm{GeV}$ by employing a minimal renormalizable superpotential coupled with a well-defined nonminimal Kähler potential. The tensor-to-scalar ratio $r$, a canonical measure of primordial gravity waves, in most cases is less than or of the order of ${10}^{-6}–{10}^{-3}$.

Magnetic fields present before decoupling are damped due to radiative viscosity. This energy injection affects the thermal and ionization history of the cosmic plasma. The implications for the CMB anisotropies and polarization are investigated for different parameter choices of a nonhelical stochastic magnetic field. Assuming a Gaussian smoothing scale determined by the magnetic damping wave number at recombination, it is found that magnetic fields with present-day strength less than 0.1 nG and negative magnetic spectral indices have a sizable effect on the CMB temperature anisotropies and polarization.

The primordial non-Gaussianity induces scale-dependent bias of the Hi with respect to the underlying dark matter, which exhibits features on the very large scale of the 21-cm power spectrum potentially observable with Hi intensity mapping observations. We forecast the prospective constraints on the four fundamental shapes of primordial non-Gaussianity (local, equilateral, orthogonal, and enfolded), with the current and future Hi intensity mapping experiments, BINGO, FAST, and SKA-I. With the current configuration of the experiments and assumed one-year observation time, we find that the SKA-I will provide tighter constraints on the local shape of primoridal non-Gaussianity than Planck. The results are $({\sigma }_{f_{\mathrm{NL}}^{\text{local}}},{\sigma }_{f_{\mathrm{NL}}^{\text{equil}}},{\sigma }_{f_{\mathrm{NL}}^{\mathrm{orth}}},{\sigma }_{f_{\mathrm{NL}}^{\text{enfold}}}{)}_{\text{SKA-I}}=(0.54,86,25,43)$, $({\sigma }_{f_{\mathrm{NL}}^{\text{local}}},{\sigma }_{f_{\mathrm{NL}}^{\text{equil}}},{\sigma }_{f_{\mathrm{NL}}^{\mathrm{orth}}},{\sigma }_{f_{\mathrm{NL}}^{\text{enfold}}}{)}_{\mathrm{BINGO}}=(17,100,128,164)$, $({\sigma }_{f_{\mathrm{NL}}^{\text{local}}},{\sigma }_{f_{\mathrm{NL}}^{\text{equil}}},{\sigma }_{f_{\mathrm{NL}}^{\mathrm{orth}}},{\sigma }_{f_{\mathrm{NL}}^{\text{enfold}}}{)}_{\mathrm{FAST}}=(9.5,44,75,94)$. If the lower frequency band of FAST can be used, the constraint on local-type primordial non-Gaussianity will be ${\sigma }_{f_{\mathrm{NL}}}\sim 1.62$ which is better than Planck. In addition, if the observation time for FAST could be extended to two years, the constraint on the equilateral shape of primordial non-Gaussianity would be improved to ${\sigma }_{f_{\mathrm{NL}}}\sim 32$. Similarly, if the observational time of SKA-I could be extended to two years, the constraint on local and orthogonal shapes could be improved to 0.43 and 20, respectively, achieving better constraints than Planck.

The bulk viscosity is studied in a thermodynamically enhanced perturbative QCD (EPQ) model that includes the running of both the strong coupling and the strange quark mass. Similar to the results in other effective models, the bulk viscosity in the EPQ model is larger by 1–2 orders of magnitude compared with that in the MIT bag model. Comparison among the different models indicates that the similarity in orders is mainly due to the inclusion of interactions between quarks. When the temperature is relatively low and enters the equation of state of quark matter, the bulk viscosity can be enormously enlarged. For the analytical expression of bulk viscosity, a reasonable range of model parameters is found. Moreover, due to the enlarged bulk viscosity, the damping time of a strange star with about 2 times the solar mass can be as short as ${10}^{-3}$ second, showing that massive quark stars could reach stability quickly after some radial unstable activities.

Heavy neutrinos, a key prediction of many standard model extensions, remain some of the most searched-for objects at collider experiments. In this context, we revisit the premise that the gluon fusion production mechanism, $gg\to Z^{*}/h^{*}\to N{\nu }_{\ell }$, is phenomenologically irrelevant at the CERN LHC and report the impact of soft gluon corrections to the production cross section. We resum threshold logarithms up to next-to-next-to-next-to-leading logarithmic accuracy ($\mathrm{N}{}^3\mathrm{LL}$), thus capturing the dominant contributions to the inclusive cross section up to next-to-next-to-leading order (${\mathrm{N}}^2\mathrm{LO}$). For $m_N>150\mathrm{GeV}$ and collider energies $\sqrt{s}=7–100\mathrm{TeV}$, corrections to the Born rates span from $+160\%$ to $+260\%$. At $\sqrt{s}=14\mathrm{TeV}$, the resummed channel is roughly equal in size to the widely-believed-to-be-dominant charged-current Drell-Yan process and overtakes it outright at $\sqrt{s}\gtrsim 20–25\mathrm{TeV}$. Results are independent of the precise nature/mixing of $N$ and hold generically for other low-scale seesaws. Findings are also expected to hold for other exotic leptons and broken axial-vector currents, particularly as the $Z^{*}$ contribution identically reduces to that of a pseudoscalar.

If the standard model Higgs boson were much heavier, it would appear as a broad resonance since its decay into a pair of longitudinally polarized gauge bosons is highly enhanced. We study whether the same enhancement happens at loop level in a simple extension of the standard model with a singlet scalar boson $S$ and three vectorlike quark multiplets. In order to focus on the loop effects, we assume that $S$ does not interact with the standard model particles at tree level. Vectorlike quarks running in the loop link the singlet scalar $S$ to the standard model world. There are two kinds of loop effects in the $S$ phenomenology—the mixing with the Higgs boson and the radiative decays into $hh$, $WW$, $ZZ$, $gg$, and $\gamma \gamma$. We show that the crucial conditions for the loop-induced longitudinal polarization enhancement are the large mass differences among vectorlike quarks. The current LHC constraints from the heavy scalar searches and the Higgs precision data are shown to be very significant: the mixing angle with the Higgs boson should be smaller than about 0.1 for $m_S=750\mathrm{GeV}$.

The study of electroweak boson pair production provides a powerful test of the spontaneously broken gauge symmetry of the standard model (SM) and can be used to search for new phenomena beyond the SM. Extra neutral vector bosons $Z^{\prime }$ decaying to charged gauge vector boson pairs $W^{+}{W}^{-}$ are predicted in many scenarios of new physics, including models with an extended gauge sector. The diboson production allows us to place stringent constraints on the $Z\text{−}{Z}^{\prime }$ mixing factor $\xi$ and $Z^{\prime }$ mass, $M_{Z^{\prime }}$. We present the $Z^{\prime }$ exclusion region in the $\xi -M_{Z^{\prime }}$ plane for the first time by using data comprised of $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ and recorded by the ATLAS and CMS detectors at the CERN LHC, with integrated luminosities of 36.1 and $35.9{\mathrm{fb}}^{-1}$, respectively. The exclusion region has been significantly extended compared to that obtained from the previous analysis performed with Tevatron data as well as with LHC data collected at 7 and 8 TeV. Also, we found that these constraints on the $Z\text{−}{Z}^{\prime }$ mixing factor are more severe than those derived from the global analysis of electroweak data. Further improvement on the constraining of this mixing can be achieved from the analysis of data to be collected at higher luminosity.

We study fermions in a magnetic field in a finite-size cylinder. With the boundary condition for the fermion flux, we show that the energy spectra and the wave functions are modified by the finite-size effect; the boundary makes the degenerate Landau levels appear only partially for states with small angular momenta, while the boundary effect becomes stronger for states with large angular momenta. We find that mode accumulation at the boundary occurs for large angular momenta and that the magnetic effect is enhanced on the boundary surface. Using a simple fermionic model, we quantify the magnetic catalysis, i.e., the magnetic enhancement of the fermion pair condensation, in a finite-size cylinder. We confirm that the magnetic catalysis is strongly amplified at the boundary due to the mode accumulation.

Rare ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{l}^{+}{l}^{-}$ and ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }\gamma$ decays are investigated in the relativistic quark model based on the quark-diquark picture of baryons. The decay form factors are calculated accounting for all relativistic effects, including relativistic transformations of baryon wave functions from rest to a moving reference frame and the contribution of the intermediate negative-energy states. The momentum-transfer-squared dependence of the form factors is explicitly determined in the whole accessible kinematical range. The calculated decay branching fractions, various forward-backward asymmetries for the rare decay ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$, are found to be consistent with recent detailed measurements by the LHCb Collaboration. Predictions for the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\tau }^{+}{\tau }^{-}$ decay observables are given.

Decays of $B^0$ and $B_s^0$ mesons to the charmless baryonic final states $p\overline{p}{h}^{+}{h}^{\prime -}$, where $h$ and $h^{\prime }$ each denote a kaon or a pion, are searched for using the LHCb detector. The analysis is based on a sample of proton-proton collision data collected at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$. Four-body charmless baryonic $B_s^0$ decays are observed for the first time. The decays $B_s^0\to p\overline{p}{K}^{+}{K}^{-}$, $B_s^0\to p\overline{p}{K}^{\pm }{\pi }^{\mp }$, $B^0\to p\overline{p}{K}^{\pm }{\pi }^{\mp }$ and $B^0\to p\overline{p}{\pi }^{+}{\pi }^{-}$ are observed with a significance greater than 5 standard deviations; evidence at 4.1 standard deviations is found for the $B^0\to p\overline{p}{K}^{+}{K}^{-}$ decay and an upper limit is set on the branching fraction for $B_s^0\to p\overline{p}{\pi }^{+}{\pi }^{-}$. Branching fractions in the kinematic region $m(p\overline{p})<2850\mathrm{MeV}/c^2$ are measured relative to the $B^0\to J/\psi (\to p\overline{p})K^{*}(892{)}^0$ channel.

The beta functions for various coupling coefficients in the Lagrangian (Appendix A in the paper) have been corrected and the updated version of the plots in the paper have been included. The conclusions of the paper remain the same.

Recently, the leading soft gluon theorem with single soft emission was shown to be the Ward identity of a two-dimensional $\mathcal{G}$-Kac-Moody symmetry. In this paper, we show that the leading soft gluon theorem can be interpreted as the Ward identity for the asymptotic symmetries of non-Abelian gauge theory. We further argue that the subleading soft gluon theorem can follow from the same symmetry.

We consider the effect of scalarization on static and slowly rotating neutron stars for a wide variety of realistic equations of state, including pure nuclear matter, nuclear matter with hyperons, hybrid nuclear and quark matter, and pure quark matter. We analyze the onset of scalarization, presenting a universal relation for the critical coupling parameter versus compactness. We find that the onset and the magnitude of the scalarization are strongly correlated with the value of the gravitational potential (the metric component $g_{tt}$) at the center of the star. We also consider the moment-of-inertia–compactness relations and confirm universality for the nuclear matter, hyperon and hybrid equations of state.

We investigate the impact of general conditions of theoretical stability and cosmological viability on dynamical dark energy models. As a powerful example, we study whether minimally coupled, single field quintessence models that are safe from ghost instabilities, can source the Chevallier-Polarski-Linder (CPL) expansion history recently shown to be mildly favored by a combination of cosmic microwave background (Planck) and weak lensing (KiDS) data. We find that in their most conservative form, the theoretical conditions impact the analysis in such a way that smooth single field quintessence becomes significantly disfavored with respect to the standard $\mathrm{\Lambda }\mathrm{CDM}$ cosmological model. This is due to the fact that these conditions cut a significant portion of the $(w_0,w_a)$ parameter space for CPL, in particular, eliminating the region that would be favored by weak lensing data. Within the scenario of a smooth dynamical dark energy parametrized with CPL, weak lensing data favors a region that would require multiple fields to ensure gravitational stability.

We show initial data for gravitational axial waves that are twice differentiable but that are not $C^2$. They generate wave pulses that interact with matter in the radiation cosmological era. This forces the radiation matter to rotate. This rotation is permanent—it persists after the passage of the gravitational pulse. The observed inhomogeneities of the cosmic microwave background radiation put a bound onto discontinuities of superhorizon metric perturbations. We explicitly show that a class of smooth initial metrics that are at least $C^2$ gives rise to gravitational wave pulses that do not interact with the background during the radiation epoch.