We find the asymptotic formula for quasinormal mode frequencies ${\omega }_n$ of the Dirac equation in a Schwarzschild-${\mathrm{AdS}}_D$ background in spacetime dimension $D>3$, in the large black-hole limit appropriate to many applications of the AdS/CFT correspondence. By asymptotic, we mean large overtone number $n$ with everything else held fixed, and we find the $O(n^0)$ correction to the known leading $O(n)$ behavior of ${\omega }_n$. The result has the schematic form ${\omega }_n\simeq n\Delta \omega +A\ln n+B$, where $\Delta \omega$ and $A$ are constants and $B$ depends logarithmically on the ($D-2$)-dimensional spatial momentum $\mathit{k}$ parallel to the horizon. We show that the asymptotic result agrees well with exact quasinormal mode frequencies computed numerically.

We consider the role of quantum effects in the nonperturbative decay of the non-Abelian string with orientational moduli in nonsupersymmetric $D=4$ gauge theory. To this aim the effective action in the $CP(N-1)$ model on a disk at large $N$ has been calculated. It exhibits a phase transition at some radius, the “wrong sign” Luscher term, and a large boundary boojumlike negative contribution. The effect of the $\theta$ term and the possibility of the spontaneous creation of the non-Abelian string are briefly discussed.

We derive the twisted-mass potential in $\mathcal{N}=(2,2)$ $C{P}^{N-1}$ theory on the world sheet of the non-Abelian string from the bulk $\mathcal{N}=2$ theory with massive (s)quarks by determining the profile functions of the adjoint fields. Although this potential was indirectly found some time ago, this is the first direct derivation from the bulk. As an application of the adjoint field profiles, we compute and confirm the $|\mu \sigma |$ potential (where $\sigma$ is a scalar field in the gauge supermultiplet), which arises in the effective two-dimensional theory on the string due to the supersymmetry breaking bulk mass term $\mu {\mathcal{A}}^2$ for the adjoint matter.

The density of states reproducing the Bekenstein-Hawking entropy-area scaling can be modeled via a nonlocal field theory. We define a diffusion process based on the kinematics of this theory and find a spectral dimension whose flow exhibits surprising properties. While it asymptotes four from above in the infrared, in the ultraviolet the spectral dimension diverges at a finite (Planckian) value of the diffusion length, signaling a breakdown of the notion of diffusion on a continuum spacetime below that scale. We comment on the implications of this minimal diffusion scale for the entropy bound in a holographic and field-theoretic context.

We examine models in which the accelerated expansion of the Universe is driven by a scalar field rolling near an inflection point in the potential. For the simplest such models, in which the potential is of the form $V(\varphi )=V_0+V_3(\varphi -{\varphi }_0{)}^3$, the scalar field can either evolve toward $\varphi ={\varphi }_0$ at late times, yielding an asymptotic de Sitter expansion, or it can transition through the inflection point, producing a transient period of acceleration. We determine the parameter ranges which produce each of these two possibilities and also map out the region in parameter space for which the equation of state of the scalar field is close to $-1$ at all times up to the present, mimicking $\Lambda \mathrm{CDM}$. We show that the latter can be consistent with either eternal or transient acceleration. More complicated inflection point models are also investigated.

We describe scalar-pseudoscalar partner degeneration at the QCD chiral transition in terms of the dominant low-energy physical states for the light quark sector. First, we obtain within model-independent one-loop chiral perturbation theory that the QCD pseudoscalar susceptibility is proportional to the quark condensate at low $T$. Next, we show that this chiral-restoring behavior for ${\chi }_P$ is compatible with recent lattice results for screening masses and gives rise to degeneration between the scalar and pseudoscalar susceptibilities $({\chi }_S,{\chi }_P)$ around the transition point, consistently with an $O(4)$-like current restoration pattern. This scenario is clearly confirmed by lattice data when we compare ${\chi }_S(T)$ with the quark condensate, expected to scale as ${\chi }_P(T)$. Finally, we show that saturating ${\chi }_S$ with the $\sigma /f_0(500)$ broad resonance observed in pion scattering and including its finite temperature dependence, allows us to describe the peak structure of ${\chi }_S(T)$ in lattice data and the associated critical temperature. This is carried out within a unitarized chiral perturbation theory scheme which generates the resonant state dynamically and is also consistent with partner degeneration.

Within the framework of the Boltzmann transport equation with a Bhatnagar-Gross-Krook collisional kernel, we study the wake potential induced by fast partons traveling through the high-temperature QCD plasma which is anisotropic in momentum space. We calculate the dielectric response function of a collisional anisotropic quark-gluon plasma for small $\xi$ (anisotropic parameter) limit. Using this, the wake potential for various combinations of the anisotropy parameter ($\xi$) and the collision rate ($\nu$) is evaluated both for parallel and perpendicular directions of motion of the fast parton. It is seen that the inclusion of the collision modifies the wake potential, and the amount, as well as the nature, of the potential depends on the combinations of $\xi$ and $\nu$.

In the color glass condensate approach to the description of high-energy heavy-ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field in order to resum the leading secular terms that result from the Weibel instability, which would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time $\tau \ll Q_s^{-1}$ shortly after the collision, in the Fock-Schwinger gauge ${\mathcal{A}}^{\tau }=0$. In this paper, we derive these fluctuations from first principles by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.

The Lee-Wick Standard Model at temperatures near the electroweak scale is considered, with the aim of studying the electroweak phase transition. While Lee-Wick theories possess states of negative norm, they are not pathological but instead are treated by imposing particular boundary conditions and using particular integration contours in the calculation of S-matrix elements. It is not immediately clear how to extend this prescription to formulate the theory at finite temperature; we explore two different pictures of finite-temperature Lee-Wick theories, and calculate the thermodynamic variables and the (one-loop) thermal effective potential. We apply these results to study the Lee-Wick Standard Model and find that the electroweak phase transition is a continuous crossover, much like in the Standard Model. However, the high-temperature behavior is modified due to cancellations between thermal corrections arising from the negative- and positive-norm states.

The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative phase space. The quantum nature and the separability of noncommutative two-mode Gaussian states are examined. It is shown that the entanglement of Gaussian states may be exclusively induced by switching on the noncommutative deformation.

We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional renormalization group as a novel technique to compute the corresponding interacting fixed point of the renormalization group flow. We explicitly evaluate critical exponents and compare them to the exact results. The functional renormalization group method allows a generalization to tensor models for higher-dimensional quantum gravity and to group field theories. As a simple example of how this method works for such models, we compute the leading-order beta function for a colored matrix model that is inspired by recent developments in tensor models.

We compute the critical density of collapse for spherically symmetric overdensities in a class of $f(R)$ modified gravity models. For the first time we evolve the Einstein, scalar field and nonlinear fluid equations, making the minimal simplifying assumptions that the metric potentials and scalar field remain quasistatic throughout the collapse. Initially evolving a top-hat profile, we find that the density threshold for collapse depends significantly on the initial conditions imposed, specifically the choice of size and shape. By imposing “natural” initial conditions, we obtain a fitting function for the spherical collapse ${\delta }_c$ as a function of collapse redshift, mass of the overdensity and $f_{\mathrm{R}0}$, the background scalar field value at $z=0$. By extending ${\delta }_c$ into a drifting and diffusing barrier within the context of excursion set theory, we obtain a realistic mass function that might be used to confront this class of scalar-tensor models with observations of dark-matter halos. The proposed analytic formula for the halo mass function was tested against Monte Carlo random walks for a wide class of moving barriers and can therefore be applied to other modified gravity theories.

Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler–DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine part of the structure of the vacuum wave functional in the limit of infinitely fine triangulations of the three-sphere. In the large fluctuation regime, the nature of the wave function solution is such that a physically acceptable ground state emerges, with a finite nonperturbative correlation length naturally cutting off any infrared divergences. The location of the critical point in Newton’s constant $G_c$, separating the weak from the strong coupling phase, is obtained, and it is inferred from the general structure of the wave functional that fluctuations in the curvatures become unbounded at this point. Investigations of the vacuum wave functional further suggest that for weak enough coupling, $G<G_c$, a pathological ground state with no continuum limit appears, where configurations with small curvature have vanishingly small probability. One would then be lead to the conclusion that the weak coupling, perturbative ground state of quantum gravity is nonperturbatively unstable and that gravitational screening cannot be physically realized in the lattice theory. The results we find tend to be in general agreement with the Euclidean lattice gravity results and would suggest that the Lorentzian and Euclidean lattice formulations of gravity ultimately describe the same underlying nonperturbative physics.

We present a method for suppressing contributions from higher-order terms in perturbation theory, greatly increasing the amount of information that may be extracted from the matter power spectrum. In an evolved cosmological density field the highest density regions are responsible for the bulk of the nonlinear power. By suitably down-weighting these problematic regions we find that the one- and two-loop terms are typically reduced in amplitude by $\sim 70\%$ and $\sim 95\%$, respectively, relative to the linear power spectrum. This greatly facilitates modeling the shape of the galaxy power spectrum, potentially increasing the number of useful Fourier modes by more than 2 orders of magnitude. We provide a demonstration of how this technique allows the galaxy bias and the amplitude of linear matter perturbations ${\sigma }_8$ to be determined from the power spectrum on conventionally nonlinear scales, $0.1<k<0.7h{\mathrm{Mpc}}^{-1}$.

In bouncing cosmology, the primordial fluctuations are generated in a cosmic contraction phase before the bounce into the current expansion phase. For a nonsingular bounce, curvature and anisotropy grow rapidly during the bouncing phase, raising questions about the reliability of perturbative analysis. In this paper, we study the evolution of adiabatic perturbations in a nonsingular bounce by nonperturbative methods including numerical simulations of the nonsingular bounce and the covariant formalism for calculating nonlinear perturbations. We show that the bounce is disrupted in regions of the universe with significant inhomogeneity and anisotropy over the background energy density but is achieved in regions that are relatively homogeneous and isotropic. Sufficiently small perturbations, consistent with observational constraints, can pass through the nonsingular bounce with negligible alteration from nonlinearity. We follow scale invariant perturbations generated in a matterlike contraction phase through the bounce. Their amplitude in the expansion phase is determined by the growing mode in the contraction phase, and the scale invariance is well preserved across the bounce.

Within the framework of renormalization group improved inflationary cosmology motivated by asymptotically safe gravity, we study the dynamics of a scalar field which can be interpreted as the Higgs field. The background trajectories of this model can provide sufficient inflationary $e$-folds and a graceful exit to a radiation dominated phase. We study the possibility of generating primordial curvature perturbations through the Standard Model Higgs boson. This can be achieved under finely tuned parameter choices by making use of the modulated reheating mechanism. The primordial non-Gaussianity is expected to be sizable in this model. Though tightly constrained by the newly released Planck cosmic microwave background data, this model provides a potentially interesting connection between collider and early Universe physics.

The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a nontrivial task since galaxies and their host haloes are stochastic tracers of the nonlinear matter density field. This stochasticity is usually modeled as the Poisson shot noise, which is constant as a function of wave number with amplitude given by $1/\overline{n}$, where $\overline{n}$ is the number density of galaxies. Here we use dark matter haloes in $N$-body simulations to show evidence for deviations from this simple behavior and develop models that explain the behavior of the stochasticity on large scales. First, haloes are extended, nonoverlapping objects, i.e., their correlation function needs to go to $-1$ on small scales. This leads to a negative correction to the stochasticity relative to the Poisson value at low wave number $k$, decreasing to zero for wave numbers large compared to the inverse exclusion scale. Second, haloes show a nonlinear enhancement of clustering outside the exclusion scale, leading to a positive stochasticity correction. Both of these effects go to zero for high $k$, making the stochasticity scale dependent even for $k<0.1h{\mathrm{Mpc}}^{-1}$. We show that the corrections in the low-$k$ regime are the same in Eulerian and Lagrangian space, but that the transition scale is pushed to smaller scales for haloes observed at present time (Eulerian space), relative to the initial conditions (Lagrangian space). These corrections vary with halo mass, and we present approximate scalings with halo mass and redshift. We also discuss simple applications of these effects to galaxy samples with nonvanishing satellite fraction, where the stochasticity can again deviate strongly from the fiducial Poisson expectation. Overall, these effects affect the clustering of galaxies at a level of a few percent even on very large scales and need to be modeled properly if we want to extract high precision cosmological information from the upcoming galaxy redshift surveys.

We show that a chiral nonlinear sigma model coupled to degenerate neutrons exhibits a ferromagnetic phase at high density. The magnetization is due to the axial anomaly acting on the parallel layers of neutral pion domain walls spontaneously formed at high density. The emergent magnetic field would reach the QCD scale $\sim {10}^{19}[\mathrm{G}]$, which suggests that the quantum anomaly can be a microscopic origin of the magnetars (highly magnetized neutron stars).