We show that a version of the covariant gauge anomaly for a $3+1$-dimensional chiral fermion interacting with a non-Abelian gauge field can be obtained from the classical Hamiltonian flow of its probability distribution in phase space. The only quantum input needed is the Berry phase that arises from the direction of the spin being slaved to the particle’s momentum.

We present a general procedure to renormalize the stress tensor two-point correlation function on a Minkowski background in position space. The method is shown in detail for the case of a free massive scalar field in the standard Minkowski vacuum state, and explicit expressions are given for the counterterms and finite parts, which are in full accordance with earlier results for the massless case. For the general case in position space, only regularized—but not renormalized—results have been obtained previously. After a Fourier transformation to momentum space, we also check agreement with a previous calculation there. We generalize our results to general Hadamard states. Furthermore, the proposed procedure can presumably be generalized to the important case of an inflationary spacetime background, where the transition to momentum space is in general not possible.

We compute the Polyakov loop potential in Yang-Mills theory from the fully dressed primitively divergent correlation functions only. This is done in a variety of functional approaches ranging from functional renormalization group equations over Dyson-Schwinger equations to two-particle irreducible functionals. We present a confinement criterion that links the infrared behavior of propagators and vertices to the Polyakov loop expectation value. The present work extends the works of [J. Braun et al., Phys. Lett. B 684, 262 (2010); F. Marhauser and J. M. Pawlowski, arXiv:0812.1144; J. Braun et al., Eur. Phys. J. C 70, 689 (2010)] to general functional methods and sharpens the confinement criterion presented there. The computations are based on the thermal correlation functions in the Landau gauge calculated in [L. Fister and J. M. Pawlowski, arXiv:1112.5440; L. Fister and J. M. Pawlowski, arXiv:1112.5429; L. Fister, Ph.D. thesis, Heidelberg University, 2012].

We consider a gravitational theory in which matter is nonminimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the theory are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of theory the matter energy-momentum tensor is generally not conserved, and this nonconservation determines the appearance of an extra force acting on the particles in motion in the gravitational field. It is interesting to note that in the present gravitational theory, the extra force explicitly depends on the Ricci tensor, which entails a relevant deviation from the geodesic motion, especially for strong gravitational fields, thus rendering the possibility of a space-time curvature enhancement by the $R_{\mu \nu }{T}^{\mu \nu }$ coupling. The Newtonian limit of the theory is also considered, and an explicit expression for the extra acceleration that depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability and obtain the stability conditions of the theory with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the theory are investigated in detail for both the conservative and the nonconservative cases, and several classes of exact analytical and approximate solutions are obtained.

The motion of a small compact object in a curved background spacetime deviates from a geodesic due to the action of its own field, giving rise to a self-force. This self-force may be calculated by integrating the Green function for the wave equation over the past worldline of the small object. We compute the self-force in this way for the case of a scalar charge in Schwarzschild spacetime, making use of the semianalytic method of matched Green function expansions. Inside a local neighborhood of the compact object, this method uses the Hadamard form for the Green function in order to render regularization trivial. Outside this local neighborhood, we calculate the Green function using a spectral decomposition into poles (quasinormal modes) and a branch cut integral in the complex frequency plane. We show that both expansions overlap in a sufficiently large matching region for an accurate calculation of the self-force to be possible. The scalar case studied here is a useful and illustrative toy model for the gravitational case, which serves to model astrophysical binary systems in the extreme mass-ratio limit.

For a Kerr black hole perturbed by a particle on the “corotating” circular orbit (angular velocity equal to that of the unperturbed event horizon), the black hole remains in equilibrium in the sense that the perturbed event horizon is a Killing horizon of the helical Killing field. The associated surface gravity is constant over the horizon and should correspond to the physical Hawking temperature. We calculate the perturbation in surface gravity/temperature, finding it negative: the moon has a cooling effect on the black hole. We also compute the change in horizon angular frequency, which is positive, and the change in surface area/entropy, which vanishes.

We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe tested for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the $\ell =1$ mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.

In this paper we combine partial-wave (“modal”) methods with a wavelet analysis of the cosmic microwave background bispectrum. While utilizing a wavelet-based estimator, we demonstrate that it is possible—via a change of basis matrix—to express the estimator in terms of partial waves. Our implementation allows one to exploit the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain the amplitude of arbitrary primordial bispectra. In particular the methodology introduced here allows for a change of basis from the space of cubic wavelet statistics to partial waves, which have proven particularly useful for investigating the underlying shape governing the non-Gaussian signal. This will be particularly important for upcoming surveys such as Planck. A key advantage is the computational efficiency of calculating the inverse covariance matrix in wavelet space, producing an error bar which is close to optimal. We verify the efficacy and robustness of the method by applying it to WMAP7 data, finding $f_{\mathrm{NL}}^{\mathrm{loc}}=35.3\pm 23.6$ and $f_{\mathrm{NL}}^{\mathrm{eq}}=-160.6\pm 123.6$, after correcting for unresolved point sources.

We study the fluctuations in luminosity distance due to gravitational lensing produced both by galaxy halos and large-scale voids. Voids are represented via a “Swiss-cheese” model consisting of a $\Lambda \mathrm{CDM}$ Friedmann-Robertson-Walker background from which a number of randomly distributed, spherical regions of comoving radius 35 Mpc are removed. A fraction of the removed mass is then placed on the shells of the spheres, in the form of randomly located halos. The halos are assumed to be nonevolving and are modeled with Navarro-Frenk-White profiles of a fixed mass. The remaining mass is placed in the interior of the spheres, either smoothly distributed or as randomly located halos. We compute the distribution of magnitude shifts using a variant of the method of Holz and Wald [Phys. Rev. D 58, 063501 (1998)], which includes the effect of lensing shear. In the two models we consider, the standard deviation of this distribution is 0.065 and 0.072 magnitudes and the mean is $-0.0010$ and $-0.0013$ magnitudes, for voids of radius 35 Mpc and the sources at redshift 1.5, with the voids chosen so that 90% of the mass is on the shell today. The standard deviation due to voids and halos is a factor $\sim 3$ larger than that due to 35 Mpc voids alone with a 1 Mpc shell thickness, which we studied in our previous work. We also study the effect of the existence of evacuated voids, by comparing to a model where all the halos are randomly distributed in the interior of the sphere with none on its surface. This does not significantly change the variance but does significantly change the demagnification tail. To a good approximation, the variance of the distribution depends only on the mean column density of halos (halo mass divided by its projected area), the concentration parameter of the halos, and the fraction of the mass density that is in the form of halos (as opposed to smoothly distributed); it is independent of how the halos are distributed in space. We derive an approximate analytic formula for the variance that agrees with our numerical results to $\lesssim 20\%$ out to $z\simeq 1.5$, and that can be used to study the dependence on halo parameters.

An alternative method compute the entropy of de Sitter spacetime for dimensions higher than or equal to five is presented. It is shown that de Sitter entropy may be obtained from the Bekenstein–Hawking entropy of a lower-dimensional black hole. This result follows from the existence of a one-to-one correspondence between de Sitter and a spacetime containing a black hole localized on a $p$-brane. Under this correspondence and due to the holographic principle, the entropy of a five-dimensional de Sitter space may be obtained from that of a BTZ black hole localized on a 2-brane. For dimensions higher than five, de Sitter entropy is identified with the entropy of a Schwarzschild–de Sitter black hole localized on a ($d-3$)-brane.

The transition form factors of the semileptonic $B\to D_2^{*}(2460)\ell \overline{\nu }(\ell =\tau ,\mu ,e)$ decay channel are calculated within the framework of the three-point QCD sum rules. The fit functions of the form factors are then used to estimate the total decay width and branching ratio of this transition. The order of branching ratio shows that this channel can be detected at the LHCb.

We study the dynamics of electroweak symmetry breaking in an extension of the Standard Model where the Higgs sector is augmented by the addition of a real ($Y=0$) isospin triplet. We show that this scenario exhibits a novel, two-step electroweak phase transition, wherein the first step provides the strongly first-order transition as required for electroweak baryogenesis, followed by a second step to the Standard Model Higgs phase that also admits a cold dark matter candidate. We analyze the constraints on this scenario from recent results obtained at the Large Hadron Collider for the Higgs diphoton decay channel. We argue that this two-step scenario can be generalized to extensions of the Standard Model with additional higher-dimensional scalar multiplets that may yield realistic baryogenesis dynamics.

We reexamine the right-handed current effects in $b\to s$ transitions in nonmanifest left-right models. Using the effective Hamiltonian approach including all possible low-energy operators, we obtain especially the $B\to K\pi$ decay amplitudes including annihilation contributions, and investigate the right-handed current contributions to $CP$ asymmetries in $B\to K\pi$ decays. Taking into account the constraints from global analysis of muon decay measurements, $|V_{ub}|$ measurements in inclusive and exclusive $B$ decays, and $B_s^0-{\overline{B}}_s^0$ mixing measurements, we find the allowed regions of new physics parameters satisfying the current experimental data.

Using a coupled channel unitary approach, combining the heavy quark spin symmetry and the dynamics of the local hidden gauge, we investigate the meson-meson interaction with hidden beauty and obtain several new states. Both $I=0$ and $I=1$ states are analyzed, and it is shown that in the $I=1$ sector, the interactions are too weak to create any bound states within our framework. In total, we predict with confidence the existence of six bound states and six more possible weakly bound states. The existence of these weakly bound states depends on the influence of the coupled channel effects.

We consider the distribution of the complex phase of the fermion determinant in QCD at nonzero chemical potential and examine the physical conditions under which the distribution takes a Gaussian form. We then calculate the baryon number as a function of the complex phase of the fermion determinant and show 1) that the exponential cancellations produced by the sign problem take the form of total derivatives, and 2) that the full baryon number is orthogonal to this noise. These insights allow us to define a self-consistency requirement for measurements of the baryon number in lattice simulations.

We describe a generic mechanism by which a system of Dirac fermions in thermal equilibrium acquires electric charge in an external magnetic field. To this end the fermions should have an additional quantum number, isospin, or color and should be subject to a second magnetic field, which distinguishes the isospin or color, as well as to a corresponding isospin chemical potential. The role of the latter can be also played by a nontrivial holonomy (Polyakov loop) along the Euclidean time direction. The charge is accumulated since the degeneracies of occupied lowest Landau levels for particles of positive isospin and antiparticles of negative isospin are different. We discuss two physical systems where this phenomenon can be realized. One is monolayer graphene, where the isospin is associated with two valleys in the Brillouin zone, and the strain-induced pseudomagnetic field acts differently on charge carriers in different valleys. Another is hot QCD, for which the relevant non-Abelian field configurations with both nonzero chromomagnetic field and a nontrivial Polyakov loop can be realized as calorons—topological solutions of Yang-Mills equations at finite temperature. The induced electric charge on the caloron field configuration is studied numerically. We argue that due to the fluctuations of holonomy, the external magnetic field should tend to suppress charge fluctuations in the quark-gluon plasma and estimate the importance of this effect for off-central heavy-ion collisions.

We study unquenched QED in four dimensions using renormalized Schwinger-Dyson equations and focus on the behaviour of the fermion and photon propagators. For this purpose we use an improved Kızılersü-Pennington (KP) vertex which respects gauge invariance, multiplicative renormalizability for the massless case, agrees with perturbation theory in the weak coupling regime, and is free of kinematic singularities. We find that the KP vertex performs very well as expected especially in comparison with other vertex choices. We find that the Landau pole problem familiar from perturbative QED persists in the nonperturbative case with the renormalized inverse photon propagator having zero crossing.

We consider the Brans-Dicke Reissner-Nordström spacetime in isotropic coordinates and the electrostatic field of an electric point charge placed outside its surface of inversion. We treat the static electric point charge as a linear perturbation on the Brans-Dicke Reissner-Nordström background. We develop a method based upon the Copson method to convert the governing Maxwell equation on the electrostatic potential generated by the static electric point charge into a solvable linear second-order ordinary differential equation. We obtain a closed-form fundamental solution of the curved-space Laplace equation arising from the background metric, which is shown to be regular everywhere except at the point charge and its image point inside the surface of inversion. We also develop a method that demonstrates that the solution does not contain any other charge that may creep into the region that lies beyond the surface of inversion and which is not covered by the isotropic coordinates. The Brans-Dicke Reissner-Nordström spacetime therefore is linearly stable under electrostatic perturbations. This stability result includes the three degenerate cases of the fundamental solution that correspond to the Brans Type 1, the Reissner-Nordström and the Schwarzschild background spacetimes.

We study the collapse of a fuzzy sphere, that is a spherical membrane built out of D0-branes, in the Banks-Fischler-Shenker-Susskind model. At weak coupling, as the sphere shrinks, open strings are produced. If the initial radius is large then open string production is not important and the sphere behaves classically. At intermediate initial radius the backreaction from open string production is important but the fuzzy sphere retains its identity. At small initial radius the sphere collapses to form a black hole. The crossover between the later two regimes is smooth and occurs at the correspondence point of Horowitz and Polchinski.

The analytical understanding of quasinormal mode ringing requires an accurate knowledge of the Green’s function describing the response of the black hole to external perturbations. We carry out a comprehensive study of quasinormal mode excitation for Kerr black holes. Relying on the formalism developed by Mano, Suzuki, and Takasugi, we improve and extend previous calculations of the quasinormal mode residues in the complex frequency plane (“excitation factors $B_q$”). Using these results we compute the “excitation coefficients” $C_q$ (essentially the mode amplitudes) in the special case where the source of the perturbations is a particle falling into the black hole along the symmetry axis. We compare this calculation with numerical integrations of the perturbation equations, and we show quantitatively how the addition of higher overtones improves the agreement with the numerical waveforms. Our results should find applications in models of the ringdown stage and in the construction of semianalytical template banks for gravitational-wave detectors, especially for binaries with large mass ratios and/or fast-spinning black holes.