In this paper, we revisit scalar field theories in $d$ space-time dimensions possessing $U(N)$ global symmetry. Following our recent work [1], we consider the generating function of correlation functions of all $U(N)$-invariant, single-trace operators at the free-fixed point. The exact renormalization group equations are cast as Hamilton equations of radial evolution in a model space-time of one higher dimension, in this case ${\mathrm{AdS}}_{d+1}$. The geometry associated with the renormalization group equations is seen to emerge naturally out of the infinite jet bundle corresponding to the field theory and suggests their interpretation as higher-spin equations of motion. While the higher-spin equations we obtain are remarkably simple, they are nonlocal in an essential way. Nevertheless, solving these bulk equations of motion in terms of a boundary source, we derive the on-shell action and demonstrate that it correctly encodes all of the correlation functions of the field theory, written as “Witten diagrams.” Since the model space-time has the isometries of the fixed point, it is possible to construct new higher-spin theories defined in terms of geometric structures over other model space-times. We illustrate this by explicitly constructing the higher-spin renormalization group equations corresponding to the $z=2$ nonrelativistic free field theory in $D$ spatial dimensions. In this case, the model space-time is the Schrödinger space-time, ${\text{Schr}}_{D+3}$.

By combining a holographic $p$-wave superconductor model and a holographic ferromagnetism model, we study the coexistence and competition of ferromagnetism and $p$-wave superconductivity. It is found that the results depend on the self-interaction of magnetic moment of the complex vector field and which phase appears first. In the case where the ferromagnetic phase appears first, if the interaction is attractive, the system shows the ferromagnetism and superconductivity can coexist at low temperatures. If the interaction is repulsive, the system will only be in a pure ferromagnetic state. In the case where the superconducting phase appears first, the attractive interaction will lead to a magnetic $p$-wave superconducting phase at low temperatures. If the interaction is repulsive, the system will be in a pure $p$-wave superconducting phase or a ferromagnetic phase when the temperature is lowered.

We show how to perform accurate, nonperturbative and controlled calculations in quantum field theory in $d$ dimensions. We use the truncated conformal space approach, a Hamiltonian method which exploits the conformal structure of the UV fixed point. The theory is regulated in the IR by putting it on a sphere of a large finite radius. The quantum field theory Hamiltonian is expressed as a matrix in the Hilbert space of conformal field theory states. After restricting ourselves to energies below a certain UV cutoff, an approximation to the spectrum is obtained by numerical diagonalization of the resulting finite-dimensional matrix. The cutoff dependence of the results can be computed and efficiently reduced via a renormalization procedure. We work out the details of the method for the ${\varphi }^4$ theory in $d$ dimensions with $d$ being not necessarily integer. A numerical analysis is then performed for the specific case $d=2.5$, a value chosen in the range where UV divergences are absent. By going from weak to intermediate to strong coupling, we are able to observe the symmetry-preserving, symmetry-breaking, and conformal phases of the theory, and perform rough measurements of masses and critical exponents. As a byproduct of our investigations we find that both the free and the interacting theories in nonintegral $d$ are not unitary, which however does not seem to cause much effect at low energies.

We consider the relation between spin and the Berry-phase contribution to the anomalous velocity of massive and massless Dirac particles. We extend the Berry connection that depends only on the spatial components of the particle momentum to one that depends on the space and time components in a covariant manner. We show that this covariant Berry connection captures the Thomas-precession part of the Bargmann-Michel-Telegdi spin evolution, and contrast it with the traditional (unitary, but not naturally covariant) Berry connection that describes spin-orbit coupling. We then consider how the covariant connection enters the classical relativistic dynamics of spinning particles due to Mathisson, Papapetrou and Dixon. We discuss the problems that arise with Lorentz covariance in the massless case, and trace them mathematically to a failure of the Wigner-translation part of the massless-particle little group to be an exact gauge symmetry in the presence of interactions, and physically to the fact that the measured position of a massless spinning particle is necessarily observer dependent.

We consider a symmetric scalar theory with quartic coupling in 4 dimensions and compare the standard 2PI calculation with a modified version which uses an exact renormalization group method. The set of integral differential equations that is obtained from the exact renormalization group method truncates naturally, without the introduction of additional approximations. The results of the two methods agree well, which shows that the exact renormalization group can be used at the level of the 2PI effective action to obtain finite results without the use of counterterms. The method therefore offers a promising starting point to study the renormalization of higher order $n$PI theories.

We provide an analytical derivation of the thermoelectric transport coefficients of the simplest momentum-dissipating model in gauge/gravity where the lack of momentum conservation is realized by means of explicit graviton mass in the bulk. We rely on the procedure recently described by Donos and Gauntlett for holographic models where momentum dissipation is realized through nontrivial scalars. The analytical approach confirms and supports the results found previously by means of numerical computations and the associated holographic renormalization procedure. Importantly, it also provides a precise identification of the range of validity of the hydrodynamic approximation.

We apply the model of stimulated neutrino transitions to neutrinos traveling through turbulence on a nonconstant density profile. We describe a method to predict the location of large amplitude transitions and demonstrate the effectiveness of this method by comparing to numerical calculations using a model supernova (SN) profile. The important wavelength scales of turbulence, both those that stimulate neutrino transformations and those that suppress them, are presented and discussed. We then examine the effects of changing the parameters of the turbulent spectrum, specifically the root-mean-square amplitude and cutoff wavelength, and show how the stimulated transitions model offers an explanation for the increase in both the amplitude and number of transitions with large amplitude turbulence, as well as a suppression or absence of transitions for long cutoff wavelengths. The method can also be used to predict the location of transitions between antineutrino states which, in the normal hierarchy we are using, will not undergo Mikheev-Smirnov-Wolfenstein transitions. Finally, the stimulated neutrino transitions method is applied to a turbulent 2D supernova simulation and explains the minimal observed effect on neutrino oscillations in the simulation as being due to excessive long wavelength modes suppressing transitions and the absence of modes that fulfill the parametric resonance condition.

Using a framework based on the $1+3$ formalism we carry out a study on axially and reflection symmetric perfect and geodesic fluids, looking for possible models of sources radiating gravitational waves. Therefore, the fluid should be necessarily shearing, for otherwise the magnetic part of the Weyl tensor vanishes, leading to a vanishing of the super-Poynting vector. However, for the family of perfect, geodesic fluids considered here, it appears that all possible cases reduce to conformally flat, shear-free, vorticity-free fluids, i.e., Friedman-Robertson-Walker. The super-Poynting vector vanishes and therefore no gravitational radiation is expected to be produced. The physical meaning of the obtained result is discussed.

We construct asymptotically anti–de Sitter boson stars in Einstein-Gauss-Bonnet gravity coupled to a $\frac{D-1}{2}$-tuplet of complex massless scalar fields both perturbatively and numerically in $D=5,7,9,11$ dimensions. These solutions possess just a single helical Killing symmetry due to the choice of scalar fields. The energy density at the center of the star characterizes the solutions, and for each choice of the Gauss-Bonnet coupling $\alpha$ we obtain a one parameter family of solutions. All solutions respect the first law of thermodynamics, in the numerical case to within 1 part in $10^6$. We describe the dependence of the angular velocity, mass, and angular momentum of the boson stars on $\alpha$ and on the dimensionality. For $D\ge 7$ these quantities reach maximum values and then decrease to eventually approach finite values as the central energy density tends to infinity. In the limit of diverging central energy density, the Kretschmann invariant at the center of the boson star also diverges. This is in contrast to the $D=5$ case, where the Kretschmann invariant diverges at a finite value of the central energy density.

It is well known that in de Sitter space the (free) minimally coupled massless scalar field theory does not admit any de Sitter–invariant Hadamard state. Related to this is the fact that the propagator for the massive scalar field corresponding to the de Sitter–invariant vacuum state diverges in the massless limit, with the infrared-divergent term being a constant. Since the Faddeev-Popov ghosts for the covariantly quantized Yang-Mills theory are minimally coupled massless scalar fields, it might appear that de Sitter symmetry would be broken in the ghost sector of Yang-Mills theory in de Sitter space. It is shown in this paper that the modes responsible for de Sitter symmetry breaking can be removed in a way consistent with BRST invariance and that a de Sitter–invariant theory can be constructed. More generally, it is shown that the spatially constant modes (the zero modes) of the Faddeev-Popov ghosts can be disposed of in a wide class of spacetimes with compact spatial sections. Then, the effective theory obtained by removing the zero modes, which contains a nonlocal interaction term, is shown to be equivalent to the theory corresponding to using a Faddeev-Popov-ghost propagator with the constant infrared-divergent term removed, provided that one can freely integrate by parts in the spacetime integral at the vertex for the ghost interaction term.

We present a first numerical implementation of a new scheme by Pound et al. [1] that enables the calculation of the gravitational self-force in Kerr spacetime from a reconstructed metric-perturbation in a radiation gauge. The numerical task of the metric reconstruction essentially reduces to solving the fully separable Teukolsky equation, rather than having to tackle the linearized Einstein’s equations themselves in the Lorenz gauge, which are not separable in Kerr. The method offers significant computational saving compared to existing methods in the Lorenz gauge, and we expect it to become a main workhorse for precision self-force calculations in the future. Here we implement the method for circular orbits on a Schwarzschild background, in order to illustrate its efficacy and accuracy. We use two independent methods for solving the Teukolsky equation, one based on a direct numerical integration, and the other on the analytical approach of Mano, Suzuki, and Takasugi. The relative accuracy of the output self-force is at least $10^{-7}$ using the first method, and at least $10^{-9}$ using the second; the two methods agree to within the error bars of the first. We comment on the relation to a related approach by Shah et al. [2], and discuss foreseeable applications to more generic orbits in Kerr spacetime.

We discuss how under certain conditions the black hole information puzzle and the (related) arguments that firewalls are a typical feature of black holes can break down. We first review the arguments of Almheiri, Marolf, Polchinski and Sully favoring firewalls, focusing on entanglements in a simple toy model for a black hole and the Hawking radiation. By introducing a large and inaccessible system entangled with the black hole (representing perhaps a de Sitter stretched horizon or inaccessible part of a landscape), we show complementarity can be restored and firewalls can be avoided throughout the black hole’s evolution. Under these conditions black holes do not have an “information problem.” We point out flaws in some of our earlier arguments that such entanglement might be generically present in some cosmological scenarios and call out certain ways our picture may still be realized.

We investigate a Boltzmann gas at equilibrium with its center of mass moving on a circular geodesic in the Schwarzschild field. As a consequence of Tolman’s law we find that a central comoving observer measures oscillations of the temperature and of other thermodynamic quantities with twice the frequencies that are known from test-particle motion. We apply this scheme to the gas dynamics in the gravitational fields of the planets of the Solar System as well as to strong-field configurations of neutron stars and black holes.

The cosmology of brane-induced gravity in six infinite dimensions is investigated. It is shown that a brane with Friedmann-Robertson-Walker symmetries necessarily acts as a source of cylindrically symmetric gravitational waves, so-called Einstein-Rosen waves. Their existence essentially distinguishes this model from its codimension-one counterpart and necessitates solving the nonlinear system of bulk and brane-matching equations. A numerical analysis is performed and two qualitatively different and dynamically separated classes of cosmologies are derived: Degravitating solutions for which the Hubble parameter settles to zero despite the presence of a novanishing energy density on the brane, and superaccelerating solutions for which Hubble grows unbounded. The parameter space of both the stable and unstable regime is derived and observational consequences are discussed: It is argued that the degravitating regime does not allow for a phenomenologically viable cosmology. On the other hand, the superaccelerating solutions are potentially viable; however, their unstable behavior questions their physical relevance.

Bayesian model comparison penalizes models with more free parameters that are allowed to vary over a wide range, and thus offers the most robust method to decide whether some given data require new parameters. In this paper, we ask a simple question: do current cosmological data require extensions of the simplest single-field inflation models? Specifically, we calculate the Bayesian evidence of a totally anticorrelated isocurvature perturbation and a running spectral index of the scalar curvature perturbation. These parameters are motivated by recent claims that the observed temperature anisotropy of the cosmic microwave background on large angular scales is too low to be compatible with the simplest inflation models. Both a subdominant, anticorrelated cold dark matter isocurvature component and a negative running index succeed in lowering the large-scale temperature power spectrum. We show that the introduction of isocurvature perturbations is disfavored, whereas that of the running spectral index is only moderately favored, even when the BICEP2 data are included in the analysis without any foreground subtraction.

In this paper we explored in detail a phenomenological model of modified single field natural inflation in light of recent cosmological experiments, BICEP2. Our main goal is to construct an inflationary model which not only predicts the important cosmological quantities such as $(n_s,r)$ compatible with experimental observation, but also is consistent with the low energy effective theory framework. Therefore, all fundamental scales apart from $M_p$ and quantities of our interest should be within the sub-Planckian region. In order to achieve our goal, we modify the usual single field natural inflationary model by a specific form of higher derivative kinetic terms called kinetic gravity braiding. One of our guiding principles to construct such a model is the constant shift symmetry of the axion. We have chosen the form of the kinetic gravity braiding term in such a way that it predicts the required value of $n_s\simeq 0.96$ and a large tensor to scalar ratio, $r>0.1$. Importantly, for a wide range of parameter space our model has sub-Planckian axion decay constant $f$ and the scale of inflation $\mathrm{\Lambda }$. However, the reheating after the end of inflation limits the value of $f$ so that we are unable to get $f$ to be significantly lower than $M_p$. Furthermore, we find sub-Planckian field excursion for the axion field $\mathrm{\Delta }\varphi \simeq f$ for the sufficient number of $e$-folding, $\mathcal{N}\gtrsim 50$. We also discussed in detail about the natural preheating mechanism in our model based on the recently proposed Chern-Simon coupling. We found this gravity mediated preheating is very difficult to achieve in our model. With our general analytic argument, we also would like to emphasize that Chern-Simons mediated preheating is very unlikely to happen in any slow roll inflationary model.

We analyze the cosmological role of terminal vacua in the string theory landscape, and point out that existing work on this topic makes very strong assumptions about the properties of the terminal vacua. We explore the implications of relaxing these assumptions (by including “arrival” as well as “departure” terminals) and demonstrate that the results in earlier work are highly sensitive to their assumption of no arrival terminals. We use our discussion to make some general points about tuning and initial conditions in cosmology.

The simplest inflationary models present us with few observable parameters to discriminate between them. A detection of features in the spectra of primordial density perturbations could provide valuable insights and lead to stringent tests of models of the early Universe. So far, searches for oscillatory features have not produced statistically significant results. In this work we consider a combined search for features in the power spectrum and bispectrum. We show that possible dependencies between the estimates of feature model amplitudes based on the two- and three-point correlators are largely statistically independent under the assumption of the null hypothesis of a nearly Gaussian featureless cosmic microwave background. Building on this conclusion we propose an optimal amplitude estimator for a combined search and study the look-elsewhere effect in feature model surveys. In particular we construct analytic models for the distribution of amplitude estimates that allow for a reliable assessment of the significance of potential findings. We also propose a well-behaved integrated statistic that is designed to detect evidence for models exhibiting features at multiple frequencies.

In order to study the “Cosmic Dawn” and the Epoch of Reionization with 21 cm tomography, we need to statistically separate the cosmological signal from foregrounds known to be orders of magnitude brighter. Over the last few years, we have learned much about the role our telescopes play in creating a putatively foreground-free region called the “EoR window.” In this work, we examine how an interferometer’s effects can be taken into account in a way that allows for the rigorous estimation of 21 cm power spectra from interferometric maps while mitigating foreground contamination and thus increasing sensitivity. This requires a precise understanding of the statistical relationship between the maps we make and the underlying true sky. While some of these calculations would be computationally infeasible if performed exactly, we explore several well-controlled approximations that make mapmaking and the calculation of map statistics much faster, especially for compact and highly redundant interferometers designed specifically for 21 cm cosmology. We demonstrate the utility of these methods and the parametrized trade-offs between accuracy and speed using one such telescope, the upcoming Hydrogen Epoch of Reionization Array, as a case study.

Static thermal equilibrium of a quantum self-gravitating ideal gas in general relativity is studied at any temperature, taking into account the Tolman-Ehrenfest effect. Thermal contribution to the gravitational stability of static neutron cores is quantified. The curve of maximum mass with respect to temperature is reported. At low temperatures the Oppenheimer-Volkoff calculation is recovered, while at high temperatures the recently reported classical gas calculation is recovered. An ultimate upper mass limit $M=2.43M_{\odot }$ of all maximum values is found to occur at Tolman temperature $T=1.27{\mathrm{mc}}^2$ with radius $R=15.2\mathrm{km}$.