Accepting that galactic mass discrepancies are due to modified dynamics, I show why it is specifically the Modified Newtonian dynamics (MOND) paradigm that is pointed to cogently. MOND is thus discussed here as a special case of a larger class of modified dynamics theories whereby galactic systems with large mass discrepancies are described by scale-invariant dynamics. This is a novel presentation that uses more recent, after-the-fact insights and data (largely predicted beforehand by MOND). Starting from a purist set of tenets, I follow the path that leads specifically to the MOND basic tenets. The main signposts are as follows: (i) Space-time scale invariance underlies the dynamics of systems with large mass discrepancies. (ii) In these dynamics, $G$ must be replaced by a single “scale-invariant” gravitational constant, $Q_0$ (in MOND, $Q_0={\mathcal{A}}_0=G{a}_0$, where $a_0$ is MOND’s acceleration constant). (iii) Universality of free fall points to the constant $q_0\equiv Q_0/G$ as the boundary between the $G$-controlled, standard dynamics, and the $Q_0$-controlled, scale-invariant dynamics (in MOND, $q_0=a_0$). (iv) Data clinch the case for $q_0$ being an acceleration (MOND).

The geometry of thermodynamic state space is studied for asymptotically anti–de Sitter black holes in $D$-dimensional space-times. Convexity of thermodynamic potentials and the analytic structure of the response functions is analyzed. The thermodynamic potentials can be used to define a metric on the space of thermodynamic variables, and two commonly used such metrics are the Weinhold metric, derived from the internal energy, and the Ruppeiner metric, derived from the entropy. The intrinsic curvature of these metrics is calculated for charged and for rotating black holes, and it is shown that the curvature diverges when heat capacities diverge but, contrary to general expectations, the singularities in the Ricci scalars do not reflect the critical behavior. When a cosmological constant is included as a state space variable, it can be interpreted as a pressure and the thermodynamically conjugate variable as a thermodynamic volume. The geometry of the resulting extended thermodynamic state space is also studied, in the context of rotating black holes, and there are curvature singularities when the heat capacity at constant angular velocity diverges and when the black hole is incompressible. Again the critical behavior is not visible in the singularities of the thermodynamic Ricci scalar.

Linearized gravitational waves in de Sitter spacetime are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity. Specifically, (i) In the exact theory, the intrinsic geometry of $\mathcal{I}$ is often assumed to be conformally flat in order to reduce the asymptotic symmetry group from $\text{Diff}(\mathcal{I})$ to the de Sitter group. Our results show explicitly that this condition is physically unreasonable. (ii) We obtain expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at ${\mathcal{I}}^{+}$. (iii) We argue that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy. Finally, (iv) we demonstrate that the flux formulas reduce to the familiar ones in Minkowski spacetime in spite of the fact that the limit $\mathrm{\Lambda }\to 0$ is discontinuous (since, in particular, $\mathcal{I}$ changes its spacelike character to null in the limit).

We consider the motion of test particles in the spacetime of a black hole in $f(R)$ gravity. The complete set of analytic solutions of the geodesic equation in the spacetime of this black hole is presented. The geodesic equations are solved in terms of Weierstrass elliptic functions and derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant $(\mathrm{\Lambda })$ and the real constant $(\beta )$.

We study the dynamics of a plasma of charged relativistic fermions at very high temperature $T\gg m$, where $m$ is the fermion mass, coupled to the electromagnetic field. In particular, we derive a magnetohydrodynamical description of the evolution of such a plasma. We show that, compared to conventional magnetohydronamics (MHD) for a plasma of nonrelativistic particles, the hydrodynamical description of the relativistic plasma involves new degrees of freedom described by a pseudoscalar field originating in a local asymmetry in the densities of left-handed and right-handed fermions. This field can be interpreted as an effective axion field. Taking into account the chiral anomaly we present dynamical equations for the evolution of this field, as well as of other fields appearing in the MHD description of the plasma. Due to its nonlinear coupling to helical magnetic fields, the axion field significantly affects the dynamics of a magnetized plasma and can give rise to a novel type of inverse cascade.

Core optics components for high-precision measurements are made of stable materials, having small optical and mechanical dissipation. The natural choice in many cases is glass, in particular fused silica. Glass is a solid amorphous state of material that could not become a crystal due to high viscosity. However, thermodynamically or externally activated stimulated local processes of spontaneous crystallization (known as devitrification) are still possible. Being random, these processes can produce an additional noise, and influence the performance of such experiments as laser gravitational wave detection.

We present our study of the renormalization of the chromomagnetic operator, ${\mathcal{O}}_{\mathrm{CM}}$, which appears in the effective Hamiltonian describing $\mathrm{\Delta }S=1$ transitions in and beyond the Standard Model. We have computed, perturbatively to one loop, the relevant Green’s functions with two (quark-quark) and three (quark-quark-gluon) external fields, at nonzero quark masses, using both the lattice and dimensional regularizations. The perturbative computation on the lattice is carried out using the maximally twisted-mass action for the fermions, while for the gluons we employed the Symanzik improved gauge action for different sets of values of the Symanzik coefficients. We have identified all the operators which can possibly mix with ${\mathcal{O}}_{\mathrm{CM}}$, including lower-dimensional and nongauge invariant operators, and we have calculated those elements of the mixing matrix which are relevant for the renormalization of ${\mathcal{O}}_{\mathrm{CM}}$. We have also performed numerical lattice calculations to determine nonperturbatively the mixings of the chromomagnetic operator with lower-dimensional operators, through proper renormalization conditions. For the first time, the $1/a^2$-divergent mixing of the chromomagnetic operator with the scalar density has been determined nonperturbatively with high precision. Moreover, the $1/a$-divergent mixing with the pseudoscalar density, due to the breaking of parity within the twisted-mass regularization of QCD, has been calculated nonperturbatively and found to be smaller than its one-loop perturbative estimate. The QCD simulations have been carried out using the gauge configurations produced by the European Twisted Mass Collaboration with $N_f=2+1+1$ dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values.

We study the dependence on the quark mass of the compositeness of the lowest-lying odd parity hyperon states. Thus, we pay attention to $\mathrm{\Lambda }$-like states in the strange, charm, and beauty sectors which are dynamically generated using a unitarized meson-baryon model. In the strange sector we use a SU(6) extension of the Weinberg-Tomozawa meson-baryon interaction, and we further implement the heavy-quark spin symmetry to construct the meson-baryon interaction when charmed or beauty hadrons are involved. In the three examined flavor sectors, we obtain two $J^P=1/2^{-}$ and one $J^P=3/2^{-}$ $\mathrm{\Lambda }$ states. We find that the $\mathrm{\Lambda }$ states which are bound states (the three ${\mathrm{\Lambda }}_b$) or narrow resonances [one $\mathrm{\Lambda }(1405)$ and one ${\mathrm{\Lambda }}_c(2595)$] are well described as molecular states composed of $s$-wave meson-baryon pairs. The ${\frac{1}{2}}^{-}$ wide $\mathrm{\Lambda }(1405)$ and ${\mathrm{\Lambda }}_c(2595)$ as well as the ${\frac{3}{2}}^{-}$ $\mathrm{\Lambda }(1520)$ and ${\mathrm{\Lambda }}_c(2625)$ states display smaller compositeness so they would require new mechanisms, such as $d$-wave interactions.

The structure of the $a_0(980)$ and $f_0(980)$ resonances is investigated with the $a_0(980)\text{−}{f}_0(980)$ mixing intensity from the viewpoint of compositeness, which corresponds to the amount of two-body states composing resonances as well as bound states. For this purpose, we first formulate the $a_0(980)\text{−}{f}_0(980)$ mixing intensity as the ratio of two partial decay widths of a parent particle, in the same manner as the recent analysis in BES experiments. Calculating the $a_0(980)\text{−}{f}_0(980)$ mixing intensity with the existing Flatte parameters from experiments, we find that many combinations of the $a_0(980)$ and $f_0(980)$ Flatte parameters can reproduce the experimental value of the $a_0(980)\text{−}{f}_0(980)$ mixing intensity by BES. Next, from the same Flatte parameters, we also calculate the $K\overline{K}$ compositeness for $a_0(980)$ and $f_0(980)$. Although the compositeness with the correct normalization becomes complex in general for resonance states, we find that the Flatte parameters for $f_0(980)$ imply a large absolute value of the $K\overline{K}$ compositeness, and the parameters for $a_0(980)$ lead to a small but non-negligible absolute value of the $K\overline{K}$ compositeness. Then, connecting the mixing intensity and the $K\overline{K}$ compositeness via the $a_0(980)$- and $f_0(980)\text{−}K\overline{K}$ coupling constants, we establish a relation between them. As a result, a small mixing intensity indicates a small value of the product of the $K\overline{K}$ compositeness for the $a_0(980)$ and $f_0(980)$ resonances. Moreover, the experimental value of the $a_0(980)\text{−}{f}_0(980)$ mixing intensity implies that the $a_0(980)$ and $f_0(980)$ resonances cannot be simultaneously $K\overline{K}$ molecular states.

A real antisymmetric tensor field was introduced to realize a holographic magnetic ordered phase in our previous papers. However, a more careful analysis shows there is a vector ghost in the model. In this paper we present a modified Lagrangian density for the antisymmetric tensor, which is ghost free and causality is well defined, and keeps all the significant results in the original model qualitatively. We show this modified Lagrangian density could come from the dimensional compactification of $p$-form field in string/M theory. For static curved space-time, we also prove that this modified model is ghost free and does not violate causality. This new model offers a solid foundation for the application of antisymmetric tensor field in holographic duality, especially for the spontaneous magnetization.

In this paper we examine the properties of $U(1)$ gauged $Q$-balls in two models with different scalar field potentials. The obtained results demonstrate that in the general case $U(1)$ gauged $Q$-balls possess properties, which differ considerably from those of $Q$-balls in the nongauged case with the same forms of the scalar field potential. In particular, it is shown that in some cases the charge of $U(1)$ gauged $Q$-ball can be bounded from above, whereas it is not so for the corresponding nongauged $Q$-ball. Our conclusions are supported both by analytical considerations and numerical calculations.

The non-Abelian Josephson junction is a junction of non-Abelian color superconductors sandwiching an insulator, or a non-Abelian domain wall if flexible, whose low-energy dynamics is described by a $U(N)$ principal chiral model with the conventional pion mass. A non-Abelian Josephson vortex is a non-Abelian vortex (color magnetic flux tube) residing inside the junction, that is described as a non-Abelian sine-Gordon soliton. In this paper, we propose Josephson instantons and Josephson monopoles, that is, Yang-Mills instantons and monopoles inside a non-Abelian Josephson junction, respectively, and show that they are described as $SU(N)$ Skyrmions and $U(1{)}^{N-1}$ vortices in the $U(N)$ principal chiral model without and with a twisted-mass term, respectively. Instantons with a twisted boundary condition are reduced (or T-dual) to monopoles, implying that $\mathbb{C}{P}^{N-1}$ lumps are T-dual to $\mathbb{C}{P}^{N-1}$ kinks inside a vortex. Here we find $SU(N)$ Skyrmions are T-dual to $U(1{)}^{N-1}$ vortices inside a wall. Our configurations suggest a yet another duality between $\mathbb{C}{P}^{N-1}$ lumps and $SU(N)$ Skyrmions as well as that between $\mathbb{C}{P}^{N-1}$ kinks and $U(1{)}^{N-1}$ vortices, viewed from different host solitons. They also suggest a duality between fractional instantons and bions in the $\mathbb{C}{P}^{N-1}$ model and those in the $SU(N)$ principal chiral model.

The weak-field and slow-motion limit of $f(R,\mathcal{G})$ gravity is developed up to $(v/c{)}^4$ order in a spherically symmetric background. Considering the Taylor expansion of a general function $f$ around vanishing values of $R$ and $\mathcal{G}$, we present general vacuum solutions up to $(v/c{)}^4$ order for the gravitational field generated by a ball-like source. The spatial behaviors at $(v/c{)}^2$ order are the same for $f(R,\mathcal{G})$ gravity and $f(R)$ gravity, and their corresponding real valued static behaviors are presented and compared with the one in general relativity. The static Yukawa-like behavior is proved to be compatible with the previous result of the most general fourth-order theory. At $(v/c{)}^4$ order, the static corrections to the Yukawa-like behavior for $f(R,\mathcal{G})$ gravity, $f(R)$ gravity, and the Starobinsky gravity are presented and compared with the one in general relativity.

The standard cosmological model does not determine the spatial topology of the Universe. This article revisits the signature of a nontrivial topology on the properties of the cosmic microwave background anisotropies. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature that can be used to distinguish a multiconnected space from an infinite space on sizes larger than the last scattering surface. The effect of the instrumental noise and of a Galactic cut are estimated. We thus establish boundaries for the size of the biggest torus distinguishable with temperature and polarization CMB data. We also describe the imprint of the spatial topology on the 3-point function and on non-Gaussianity.

We exploit the recently developed software package LieART to show that $\mathrm{SU}(N)$ grand unified theories with chiral fermions in mixed tensor irreducible representations can lead to standard model chiral fermions without additional light exotic chiral fermions; i.e., only standard model fermions are light in these models. Results are tabulated which may be of use to model builders in the future. An SU(6) toy model is given and model searches are discussed.

One intriguing beyond-the-Standard-Model particle is the QCD axion, which could simultaneously provide a solution to the Strong $CP$ Problem and account for some, if not all, of the dark matter density in the Universe. This particle is a pseudo-Nambu–Goldstone boson of the conjectured Peccei–Quinn symmetry of the Standard Model. Its mass and interactions are suppressed by a heavy symmetry-breaking scale, $f_a$, the value of which is roughly greater than ${10}^9\mathrm{GeV}$ (or, conversely, the axion mass, $m_a$, is roughly less than ${10}^4\mu \mathrm{eV}$). The density of axions in the Universe, which cannot exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX, is a result of the early Universe interplay between cosmological evolution and the axion mass as a function of temperature. The latter quantity is proportional to the second derivative of the temperature-dependent QCD free energy with respect to the $CP$-violating phase, $\theta$. However, this quantity is generically nonperturbative, and previous calculations have only employed instanton models at the high temperatures of interest (roughly 1 GeV). In this and future works, we aim to calculate the temperature-dependent axion mass at small $\theta$ from first-principle lattice calculations, with controlled statistical and systematic errors. Once calculated, this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the Universe, which is required to be less than or equal to the dark matter density. Due to a variety of lattice systematic effects at the very high temperatures required, we perform a calculation of the leading small-$\theta$ cumulant of the theta vacua on large volume lattices for SU(3) Yang–Mills with high statistics as a first proof of concept, before attempting a full QCD calculation in the future. From these pure glue results, the misalignment mechanism yields the axion mass bound $m_a\ge (14.6\pm 0.1)\mu \mathrm{eV}$ when Peccei–Quinn breaking occurs after inflation.

We present the first unquenched lattice-QCD calculation of the hadronic form factors for the exclusive decay $\overline{B}\to D\ell \overline{\nu }$ at nonzero recoil. We carry out numerical simulations on 14 ensembles of gauge-field configurations generated with $2+1$ flavors of asqtad-improved staggered sea quarks. The ensembles encompass a wide range of lattice spacings (approximately 0.045 to 0.12 fm) and ratios of light (up and down) to strange sea-quark masses ranging from 0.05 to 0.4. For the $b$ and $c$ valence quarks we use improved Wilson fermions with the Fermilab interpretation, while for the light valence quarks we use asqtad-improved staggered fermions. We extrapolate our results to the physical point using rooted staggered heavy-light meson chiral perturbation theory. We then parametrize the form factors and extend them to the full kinematic range using model-independent functions based on analyticity and unitarity. We present our final results for $f_{+}(q^2)$ and $f_0(q^2)$, including statistical and systematic errors, as coefficients of a series in the variable $z$ and the covariance matrix between these coefficients. We then fit the lattice form-factor data jointly with the experimentally measured differential decay rate from BABAR to determine the CKM matrix element, $|V_{cb}|=(39.6\pm 1.7_{\mathrm{QCD}+\exp }\pm 0.2_{\mathrm{QED}})\times {10}^{-3}$. As a byproduct of the joint fit we obtain the form factors with improved precision at large recoil. Finally, we use them to update our calculation of the ratio $R(D)$ in the Standard Model, which yields $R(D)=0.299(11)$.

The decay $K_L\to \mathit{\text{invisible}}$ has never been experimentally tested. In the Standard Model (SM), its branching ratio for the decay into two neutrinos is helicity suppressed and predicted to be $\mathrm{Br}(K_L\to \nu \overline{\nu })\lesssim {10}^{-10}$. We consider several natural extensions of the SM, such as two-Higgs-doublet (2HDM), 2HDM and light scalar, and mirror dark matter models, whose main feature is that they allow us to avoid the helicity suppression factor and lead to an enhanced $\mathrm{Br}(K_L\to \mathit{\text{invisible}})$. For the decay $K_L\to \nu \overline{\nu }$, the smallness of the neutrino mass in the considered 2HDM model is explained by the smallness of the second Higgs doublet vacuum expectation value. The small nonzero value of the second Higgs isodoublet can arise as a consequence of nonzero quark condensate. We show that taking into account the most stringent constraints from the $K\to \pi +\mathit{\text{invisible}}$ decay, this process could be in the region of $\mathrm{Br}(K_L\to \mathit{\text{invisible}})\simeq {10}^{-8}–{10}^{-6}$, which is experimentally accessible. In some scenarios, the $K_L\to \mathit{\text{invisible}}$ decay could still be allowed while the $K\to \pi +\mathit{\text{invisible}}$ decay is forbidden. The results obtained show that the $K_L\to \mathit{\text{invisible}}$ decay is a clean probe of new physics scales well above 100 TeV that is complementary to rare $K\to \pi +\mathit{\text{invisible}}$ decay, and they provide a strong motivation for its sensitive search in a near-future experiment.

We make predictions for ratios of branching fractions of ${\overline{B}}^0$ decays into $D^0$ and the scalar mesons $f_0(500)$, $f_0(980)$, $a_0(980)$, plus ${\overline{B}}_s^0$ decay into $D^0$ and $\kappa (800)$. We also compare the ${\pi }^{+}{\pi }^{-}$ production in the scalar channel with that observed in the $\rho$ channel and make predictions for the ${\overline{B}}_s^0$ decay into $D^0$ and $K^{*}(892)$, comparing the strength of this channel with that of $\kappa (800)$ production. The work is based on results of the chiral unitary approach where the scalar resonances are generated from the pseudoscalar-pseudoscalar interaction. Up to an arbitrary normalization, the mass distributions and rates for decays into the scalar resonances are predicted with no free parameters. Comparison with experimental data is done when available.