We introduce the notion of a local shadow for a black hole and determine its shape for the particular case of a distorted Schwarzschild black hole. Considering the lowest-order even and odd multiple moments, we compute the relation between the deformations of the shadow of a Schwarzschild black hole and the distortion multiple moments. For the range of values of multiple moments that we consider, the horizon is deformed much less than its corresponding shadow, suggesting the horizon is more “rigid.” Quite unexpectedly, we find that a prolate distortion of the horizon gives rise to an oblate distortion of the shadow and vice versa.

Bose-Einstein condensates (BECs) have been proposed as candidate states of matter for the interior of neutron stars. Specifically, Chavanis and Harko obtained the mass-radius relation for a BEC star and proposed that the recently discovered neutron stars with masses around $2M_{\odot }$ are BEC stars. They employed a barotropic equation of state (EOS), with one free parameter, that was first found by Colpi, Shapiro, and Wasserman (CSW), to describe them and derive stable equilibrium configurations of spinning BEC stars in general relativity. In this work we show that while it is true that BECs allow for compact object masses as heavy as the heaviest observed ones, such stars cannot simultaneously have radii that are small enough to be consistent with the latest observations, in spite of the flexibility available in the EOS in the form of the free parameter. In fact, our conclusion applies to any spinning relativistic boson star that obeys the CSW EOS.

Cosmological inflation is discussed in the framework of $F(R,\mathcal{G})$ gravity where $F$ is a generic function of the curvature scalar $R$ and the Gauss–Bonnet topological invariant $\mathcal{G}$. The main feature that emerges in this analysis is the fact that this kind of theory can exhaust all the curvature budget related to curvature invariants without considering derivatives of $R$, $R_{\mu \nu }$, $R_{\sigma \mu \nu }^{\lambda }$, etc., in the action. Cosmological dynamics results driven by two effective masses (lengths) are related to the $R$ scalaron and the $\mathcal{G}$ scalaron working respectively at early and very early epochs of cosmic evolution. In this sense, a double inflationary scenario naturally emerges.

Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of $O(10)$ correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.

Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. The topology of an algebraic variety characterizes the difficulty of applying maximal cuts. In this work, we analyze a novel class of integrals of which the maximal cuts give rise to an algebraic variety with irrational irreducible components. As a phenomenologically relevant example, we examine the two-loop planar double-box contribution with internal massive lines. We derive unique projectors for all four master integrals in terms of multivariate residues along with Weierstrass’ elliptic functions. We also show how to generate the leading-topology part of otherwise infeasible integration-by-parts identities analytically from exact meromorphic differential forms.

We explore realizations of minimal flavor violation (MFV) for leptons in the simplest seesaw models where the neutrino mass generation mechanism is driven by new fermion singlets (type I) or triplets (type III) and by a scalar triplet (type II). We also discuss similarities and differences of the MFV implementation among the three scenarios. To study the phenomenological implications, we consider a number of effective dimension-six operators that are purely leptonic or couple leptons to the standard model gauge and Higgs bosons and evaluate constraints on the scale of MFV associated with these operators from the latest experimental information. Specifically, we employ the most recent measurements of neutrino mixing parameters as well as the currently available data on flavor-violating radiative and three-body decays of charged leptons, $\mu \to e$ conversion in nuclei, the anomalous magnetic moments of charged leptons, and their electric dipole moments. The most stringent lower limit on the MFV scale comes from the present experimental bound on $\mu \to e\gamma$ and can reach 500 TeV or higher, depending on the details of the seesaw scheme. With our numerical results, we illustrate some important differences among the seesaw types. In particular, we show that in types I and III there are features which can bring about potentially remarkable effects which do not occur in type II. In addition, we comment on how one of the new effective operators can induce flavor-changing dilepton decays of the Higgs boson, which may be probed in upcoming searches at the LHC.

The chirally symmetric overlap quark propagator is explored in Coulomb gauge for the first time. This gauge is especially well suited for studying the interrelation between confinement and chiral symmetry breaking, since confinement can be attributed to the infrared divergence of the vector dressing function of the inverse quark propagator. Using quenched gauge field configurations on a ${20}^4$ lattice, the dressing functions of the quark propagator as well as the dynamical quark mass function are evaluated, also in the chiral limit. Chiral symmetry is artificially restored by removing the low-mode contribution from the quark propagator. After removing enough low-lying modes, the dynamical quark mass function approaches the current quark mass in the whole momentum region and goes to zero in the chiral limit. However, the vector dressing function is unaffected by the low-mode removal. It follows that the quark energy dispersion is still infrared divergent and quarks in such a chiral symmetry restored phase are still confined within a hadron.

We determine the decay rate to leptons of the ground-state $\mathrm{\Upsilon }$ meson and its first radial excitation in lattice QCD for the first time. We use radiatively improved nonrelativistic QCD for the $b$ quarks and include $u$, $d$, $s$ and $c$ quarks in the sea with $u/d$ masses down to their physical values. We find $\mathrm{\Gamma }(\mathrm{\Upsilon }\to e^{+}{e}^{-})=1.19(11)\mathrm{keV}$ and $\mathrm{\Gamma }({\mathrm{\Upsilon }}^{\prime }\to e^{+}{e}^{-})=0.69(9)\mathrm{keV}$, both in good agreement with experimental results. The decay constants we obtain are included in a summary plot of meson decay constants from lattice QCD given in the Conclusions. We also test time moments of the vector current-current correlator against values determined from the $b$-quark contribution to $\sigma (e^{+}{e}^{-}\to \text{hadrons})$ and calculate the $b$-quark piece of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_{\mu }^b=0.271(37)\times 10^{-10}$. Finally we determine the $b$-quark mass, obtaining in the $\overline{\mathrm{MS}}$ scheme, ${\overline{m}}_b({\overline{m}}_b,n_f=5)=4.196(23)\mathrm{GeV}$, the most accurate result from lattice QCD to date.

Measurement of the self-coupling of the 125 GeV Higgs boson is one of the most crucial tasks for a high luminosity run of the LHC, and it can only be measured in the di-Higgs final state. In the minimal supersymmetric standard model, heavy $CP$ even Higgs ($H$) can decay into a lighter 125 GeV Higgs boson ($h$) and, therefore, can influence the rate of di-Higgs production. We investigate the role of single $H$ production in the context of measuring the self-coupling of $h$. We have found that the $H\to hh$ decay can change the value of Higgs ($h$) self-coupling substantially, in a low $\tan \beta$ regime where the mass of the heavy Higgs boson lies between 250 and 600 GeV and, depending on the parameter space, it may be seen as an enhancement of the self-coupling of the 125 GeV Higgs boson.

Inspired by the holographic computation of large interval entanglement entropy of two-dimensional (2D) conformal field theory at high temperature, it was proposed that the thermal entropy is related to the entanglement entropy as $S_{th}=\underset{l\to 0}{\lim }(S_{EE}(R-l)-S_{EE}(l))$. In this paper, we prove this relation for 2D CFT with a discrete spectrum in two different ways. Moreover, we discuss this relation for a 2D noncompact free scalar, which is a gapless CFT with continuous spectrum. We show that it could be recovered, after appropriately regularizing the theory.

We study the tensor gauge fields (“notophs”) of ungauged $\mathcal{N}=8,D=4$ supergravity in superspace. These are described by 2-form potentials $B_2^G$ in the adjoint representation of $G=E_{7(+7)}$. The consistency of the natural candidates for the superspace constraints for their field strengths $H_3^G$ fixes the form of the generalized Bianchi identities $D{H}_3^G=\dots$ and also requires the potentials $B_2^{G/H}$ with indices of $G/H=E_{7(+7)}/SU(8)$ generators to be dual to the scalars of the $\mathcal{N}=8,D=4$ supergravity multiplet. In contrast, the field strengths of the 2-form potentials corresponding to the $SU(8)$ generators are dual to fermionic bilinears, so that these potentials are auxiliary rather than physical fields. Their presence, however, is essential to formulate a tensor hierarchy of $\mathcal{N}=8,D=4$ supergravity consistent with its U-duality group $E_{7(+7)}$.

It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system’s dynamical variables that maintain the form of the action principle comprises the group of canonical transformations. In the context of canonical field theory, the adjective “extended” signifies that not only the fields but also the space-time geometry is subject to transformation. Thus, in order to be physical, the transition to another, possibly noninertial frame of reference must necessarily constitute an extended canonical transformation that defines the general mapping of the connection coefficients, hence the quantities that determine the space-time curvature and torsion of the respective reference frame. The canonical transformation formalism defines simultaneously the transformation rules for the conjugates of the connection coefficients and for the Hamiltonian. As will be shown, this yields unambiguously a particular Hamiltonian that is form-invariant under the canonical transformation of the connection coefficients and thus satisfies the general principle of relativity. This Hamiltonian turns out to be a quadratic function of the curvature tensor. Its Legendre-transformed counterpart then establishes a unique Lagrangian description of the dynamics of space-time that is not postulated but derived from basic principles, namely the action principle and the general principle of relativity. Moreover, the resulting theory satisfies the principle of scale invariance and is renormalizable.

We derive light-cone cubic interaction vertices involving fermions and bosons of arbitrary spin by demanding closure of the Poincaré algebra. We derive the three-point scattering amplitude corresponding to these interaction vertices and find that they possess interesting factorization properties identical to the case of three-boson scattering.

Maximal Abelian gauge has been a particular choice to study dynamical generation of off-diagonal gluon masses in QCD. This gauge is a special case of an Abelian projection. Abelian dominance is characterized by off-diagonal gluons acquiring masses in the relevant phase. Here we propose a gauge condition which is quadratic in fields and which does not fall in the class of an Abelian projection. We explore the possible vacua of the gauge-fixed effective action of the theory and find evidence that ghost bilinears may be subject to condensation, which would signal acquisition of masses by off-diagonal gluons. Such a vacuum satisfies the requirement of Abelian dominance, providing an example of the hypothesis through a mechanism other than Abelian projection.

Starting from the Heisenberg-Euler effective Lagrangian, we determine the photon current and photon polarization tensor in inhomogeneous, slowly varying electromagnetic fields. To this end, we consider background field configurations varying in both space and time, paying special attention to the tensor structure. As a main result, we obtain compact analytical expressions for the photon polarization tensor in realistic Gaussian laser pulses, as generated in the focal spots of high-intensity lasers. These expressions are of utmost importance for the investigation of quantum vacuum nonlinearities in realistic high-intensity laser experiments.

A covariant action principle for ideal relativistic magnetohydrodynamics in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al. [Ann. Phys. 169, 29 (1986)], which uses a noncanonical bracket to effect constrained variations of an action functional. Various implications and extensions of this action principle are also discussed. Two significant byproducts of this formalism are the introduction of a new divergence-free 4-vector variable for the magnetic field, and a new Lie-dragged form for the theory.

New exact solutions to the field equations in the Einstein-Gauss-Bonnet modified theory of gravity for a five-dimensional spherically symmetric static distribution of a perfect fluid are obtained. The Frobenius method is used to obtain this solution in terms of an infinite series. Exact solutions are generated in terms of polynomials from the infinite series. The five-dimensional Einstein solution is also found by setting the coupling constant to zero. All models admit a barotropic equation of state. Linear equations of state are admitted in particular models with the energy density profile of isothermal distributions. We examine the physicality of the solution by studying graphically the isotropic pressure and the energy density. The model is well behaved in the interior, and the weak, strong, and dominant energy conditions are satisfied.

We consider higher-derivative quantum gravity where the renormalization-group-improved effective action beyond the one-loop approximation is derived. Using this effective action, the quantum-corrected Friedmann-Robertson-Walker (FRW) equations are analyzed. The de Sitter universe solution is found. It is demonstrated that such a de Sitter inflationary universe is unstable. The slow-roll inflationary parameters are calculated. The contribution of the renormalization-group-improved Gauss-Bonnet term to the quantum-corrected FRW equations as well as to the instability of the de Sitter universe is estimated. It is demonstrated that in this case, the spectral index and tensor-to-scalar ratio are consistent with Planck data.

We describe a simple class of cosmological models called $\alpha$-attractors, which provide an excellent fit to the latest Planck data. These theories are most naturally formulated in the context of supergravity with logarithmic Kähler potentials. We develop generalized versions of these models which can describe not only inflation but also dark energy and supersymmetry breaking.

We assess two potential signals of the formation of our universe by the decay of a false vacuum. Negative spatial curvature is one possibility, but the window for its detection is now small. However, another possible signal is a suppression of the cosmic microwave background (CMB) power spectrum at large angles. This arises from the steepening of the effective potential as it interpolates between a flat inflationary plateau and the high barrier separating us from our parent vacuum. We demonstrate that these two effects can be parametrically separated in angular scale. Observationally, the steepening effect appears to be excluded at large $\ell$; but it remains consistent with the slight lack of power below $\ell \approx 30$ found by the WMAP and Planck collaborations. We give two simple models which improve the fit to the Planck data; one with observable curvature and one without. Despite cosmic variance, we argue that future CMB polarization and most importantly large-scale structure observations should be able to corroborate the Planck anomaly if it is real. If we further assume the specific theoretical setting of a landscape of metastable vacua, as suggested by string theory, we can estimate the probability of seeing a low-$\ell$ suppression in the CMB. There are significant theoretical uncertainties in such calculations, but we argue the probability for a detectable suppression may be as large as $O(1)$, and in general is significantly larger than the probability of seeing curvature.