When a continuous symmetry is spontaneously broken in nonrelativistic theories, there appear Nambu-Goldstone (NG) modes, the dispersion relations of which are either linear (type I) or quadratic (type II). We give a general framework to interpolate between relativistic and nonrelativistic NG modes, revealing a nature of type-I and -II NG modes in nonrelativistic theories. The interpolating Lagrangians have the nonlinear Lorentz invariance which reduces to the Galilei or Schrödinger invariance in the nonrelativistic limit. We find that type-I and type-II NG modes in the interpolating region are accompanied with a Higgs mode and a chiral NG partner, respectively, both of which are gapful. In the ultrarelativistic limit, a set of a type-I NG mode and its Higgs partner remains, while a set of a type-II NG mode and its gapful NG partner turns to a set of two type-I NG modes. In the nonrelativistic limit, the both types of accompanied gapful modes become infinitely massive, disappearing from the spectrum. The examples contain a phonon in Bose–Einstein condensates or helium superfluids, a phonon and magnon in spinor Bose–Einstein condensates, a magnon in ferromagnets, and a kelvon and dilaton-magnon localized around a Skyrmion line in ferromagnets.

A particle in a uniformly accelerated motion exhibits Brownian random motions around the classical trajectory due to the coupling to the field vacuum fluctuations. Previous works show that the Brownian random motions satisfy the energy equipartition relation. This thermal property is understood as the consequence of the Unruh effect. In the present work, we investigate the radiation from the thermal random motions of an accelerated particle coupled to vacuum fluctuations. The energy flux of this radiation is negative of the order smaller than the classical radiation by the factor $a/m$, where $a$ is the acceleration constant and $m$ is the mass of a particle. The results could be understood as a suppression of the classical radiation by the quantum effect.

We study the Hawking radiation in field theories which break Lorentz invariance via dissipative effects above a certain energy scale. We assume that the additional degrees of freedom which cause dissipation are Gaussian and freely falling. The asymptotic spectrum and the correlations are extracted from the anticommutator of the radiation field. The singular behavior of the Green function found for relativistic fields as one point crosses the horizon is completely suppressed by dissipation. Yet, when the dissipative frequency scale is much larger than the surface gravity of the black hole, we show that the asymptotic observables acquire their standard (relativistic) vacuum expectation values. We explicitly compute the effects of dissipation on the spectrum and on the nonseparable character of the correlations when varying the dissipative scale, the extension of the near-horizon geometry, and the temperature of the environment.

We present new traversable wormhole and nonsingular black hole solutions in pure, scale-free $R^2$ gravity. These exotic solutions require no null energy condition violating or “exotic” matter and are supported only by the vacuum of the theory. It is well known that $f(R)$ theories of gravity may be recast as dual theories in the Einstein frame. The solutions we present are found when the conformal transformation required to move to the dual frame is singular. For quadratic $R^2$ gravity, the required conformal factor is identically zero for spacetimes with $R=0$. Solutions in this case are argued to arise in the strong coupling limit of general relativity.

Large-scale peculiar motions are believed to reflect the local inhomogeneity and anisotropy of the Universe, triggered by the ongoing process of structure formation. As a result, realistic observers do not follow the smooth Hubble flow but have a peculiar “tilt” velocity relative to it. Our local group of galaxies, in particular, moves with respect to the universal expansion at a speed of roughly $600\mathrm{km}/\sec$. Relative motion effects are known to interfere with the observations and their interpretation. The strong dipolar anisotropy seen in the cosmic microwave background, for example, is not treated as a sign of real universal anisotropy, but as a mere artifact of our peculiar motion relative to the Hubble flow. With these in mind, we look into the implications of large-scale bulk motions for the kinematics of their associated observers, by adopting a tilted Friedmann model. Our aim is to examine whether the deceleration parameter measured in the rest frame of the bulk flow can differ from that of the actual Universe due to relative-motion effects alone. We find that there is a difference, which depends on the speed as well as the scale of the bulk motion. The faster and the smaller the drifting domain, the larger the difference. In principle, this allows relatively slow peculiar velocities to have a disproportionately strong effect on the value of the deceleration parameter measured by observers within bulk flows of, say, a few hundred megaparsecs. In fact, under certain circumstances, it is even possible to change the sign of the deceleration parameter. It goes without saying that all these effects vanish identically in the Hubble frame, which makes them an illusion and mere artifact of the observers’ relative motion.

We consider an Einstein-scalar-Gauss-Bonnet gravitational theory, and argue that at early times the Ricci scalar can be safely ignored. We then demonstrate that the pure scalar-Gauss-Bonnet theory, with a quadratic coupling function, naturally supports inflationary—de Sitter—solutions. During inflation, the scalar field decays exponentially and its effective potential remains always bounded. The theory also contains solutions where these de Sitter phases possess a natural exit mechanism and are replaced by linearly expanding—Milne—phases.

Cosmological $\alpha$ attractors give a natural explanation for the spectral index $n_s$ of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio $r$, consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial role of the hyperbolic geometry of the Poincaré disk or half plane in the supergravity construction. These geometries are isometric under Möbius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kähler potential frame that explicitly preserves this symmetry, enabling the inflaton to be light. Moreover, we include higher-order curvature deformations, which can stabilize a direction orthogonal to the inflationary trajectory. We illustrate this new framework by stabilizing the single superfield $\alpha$ attractors.

We study the lattice artifacts of the Wilson-Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following spectral observables: the level density of the Hermitian Wilson-Dirac operator, the distribution of chirality over the real eigenvalues, and the chiral condensate for the quenched as well as for the unquenched theory. We provide analytical expressions for all these quantities. Moreover we derive constraints for the level density of the real eigenvalues of the non-Hermitian Wilson-Dirac operator and the number of additional real modes. The latter is a good measure for the strength of lattice artifacts. All computations are confirmed by Monte Carlo simulations of the corresponding random matrix theory which agrees with chiral perturbation theory of two color QCD with Wilson fermions.

We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called “special” loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the nonsymmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of these operators on a general level.

We test the validity of Isaacson’s formula which states that high frequency and low amplitude gravitational waves behave as a radiation fluid on average. For this purpose, we numerically construct a solution of the vacuum Einstein equations which contains nonlinear standing gravitational waves. The solution is constructed in a cubic box with periodic boundary conditions. The time evolution is solved in a gauge in which the trace of the extrinsic curvature $K$ of the time slice becomes spatially uniform. Then, the Hubble expansion rate $H$ is defined by $H=-K/3$ and compared with the effective scale factor $L$ defined by the proper volume, area and length of the cubic box. We find that, even when the wave length of the gravitational waves is comparable to the Hubble scale, the deviation from Isaacson’s formula $H\propto L^{-2}$ is at most 3% without taking a temporal average and is below 0.1% with a temporal average.

We consider $\mathrm{\Lambda }=0$ three-dimensional gravity with asymptotically flat boundary conditions. This system was studied by Ashtekar and Varadarajan within the second-order formalism—with metric variables—who showed that the Regge-Teitelboim formalism yields a consistent Hamiltonian description where, surprisingly, the energy is bounded from below and from above. The energy of the spacetime is, however, determined up to an arbitrary constant. The natural choice was to fix that freedom such that Minkowski spacetime has zero energy. More recently, Marolf and Patiño started from the Einstein-Hilbert action supplemented with the Gibbons-Hawking term and showed that, in the ($2+1$) decomposition of the theory, the energy is shifted from the Ashtekar-Varadarajan analysis in such a way that Minkowski spacetime possesses a negative energy. In this contribution we consider the first-order formalism, where the fundamental variables are a $so(2,1)$ connection ${{w_a}^I}_J$ and a triad $e_a^I$. We consider two actions. A natural extension to 3 dimensions of the consistent action in $4D$ Palatini gravity is shown to be finite and differentiable. For this action, the ($2+1$) decomposition (that we perform using two methods) yields a Hamiltonian boundary term that corresponds to energy. It assigns zero energy to Minkowski spacetime. We then put forward a totally gauge invariant action and show that it is also well defined and differentiable. Interestingly, it turns out to be related, on shell, to the 3D Palatini action by an additive constant in such a way that its associated energy is given by the Marolf-Patiño expression. Thus, we conclude that, from the perspective of the first-order formalism, Minkowski spacetime can consistently have either zero, or a negative energy equal to $-1/4G$, depending on the choice of consistent action employed as starting point.

We present a heuristic argument for the universal area product: $A_{+}{A}_{-}=(8\pi J{)}^2+(4\pi Q^2{)}^2$ for a four-dimensional, stationary, axisymmetric, electrically charged black hole with an arbitrary stationary axisymmetric distribution of external matter (possibly charged), derived by Marcus Ansorg and Jörg Hennig. Here $A_{+}$ and $A_{-}$ are the areas of the event and Cauchy horizons, and $J$ and $Q$ are the angular momentum and electric charge. Based on this argument, we conjecture that a universal area product holds for higher-dimensional, stationary, multihorizon black objects in the presence of an external stationary charged distribution of matter.

We study the dominant effect of a long wavelength density perturbation $\delta ({\lambda }_L)$ on short distance physics. In the nonrelativistic limit, the result is a uniform acceleration, fixed by the equivalence principle, and typically has no effect on statistical averages due to translational invariance. This same reasoning has been formalized to obtain a “consistency condition” on the cosmological correlation functions. In the presence of a feature, such as the acoustic peak at ${\ell }_{\mathrm{BAO}}$, this naive expectation breaks down for ${\lambda }_L<{\ell }_{\mathrm{BAO}}$. We calculate a universal piece of the three-point correlation function in this regime. The same effect is shown to underlie the spread of the acoustic peak, and is calculable to all orders in the long modes. This can be used to improve the result of perturbative calculations—a technique known as “infra-red resummation”—and is explicitly applied to the one-loop calculation of the power spectrum. Finally, the success of baryon acoustic oscillation reconstruction schemes is argued to be another empirical evidence for the validity of the results.

We investigate the dynamics of a neutral and a charged particle around a black hole in modified gravity immersed in a magnetic field. Our focus is on the scalar-tensor-vector theory as modified gravity. We are interested in exploring the conditions on the energy of the particle under which it can escape to infinity after collision with another neutral particle in the vicinity of the black hole. We calculate the escape velocity of particle orbiting in the innermost stable circular orbit (ISCO) after the collision. We study the effects of modified gravity on the dynamics of particles. Further, we discuss how the presence of a magnetic field in the vicinity of a black hole affects the motion of the orbiting particle. We show that the stability of ISCO increases due to the presence of a magnetic field. It is observed that a particle can go arbitrarily close to the black hole due to the presence of a magnetic field. Furthermore, ISCO for a black hole is more stable as compared with a Schwarzschild black hole. We also discuss the Lyapunov exponent and the effective force acting on the particle in the presence of a magnetic field.

In this paper, I show that backward (in time) running states can be explicitly accounted for by expanding the interpolator basis in the variational method in lattice QCD. The backward running states can then be removed by choosing an appropriate linear combination of interpolators, which improves the signal significantly. The proof of principle, which also makes use of the time-shift trick (generalized pencil-of-functions method), will be delivered at an example on a ${64}^4$ lattice close to the physical pion mass.

We study the baryonic three-quark (3Q) potential and its Abelian projection in terms of the dual-superconductor picture in SU(3) quenched lattice QCD. The non-Abelian SU(3) gauge theory is projected onto Abelian ${\mathrm{U}(1)}^2$ gauge theory in the maximal Abelian gauge. We investigate the 3Q potential and its Abelian part for more than 300 different patterns of static 3Q systems in total at $\beta =5.8$ on ${16}^{3}32$ and at $\beta =6.0$ on ${20}^{3}32$ with 1000–2000 gauge configurations. For all the distances, both the 3Q potential and Abelian part are found to be well described by the Y ansatz, i.e., two-body Coulomb term plus three-body Y-type linear term ${\sigma }_{3\mathrm{Q}}{L}_{\min }$, where $L_{\min }$ is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension ${\sigma }_{3\mathrm{Q}}$ and its Abelian part ${\sigma }_{3\mathrm{Q}}^{\text{Abel}}$ with an accuracy within a few percent deviation, i.e., ${\sigma }_{3\mathrm{Q}}\simeq {\sigma }_{3\mathrm{Q}}^{\text{Abel}}$, which means Abelian dominance of the quark-confining force in 3Q systems.

We study the property of the $X(3872)$ meson by analyzing the $B\to KD{\overline{D}}^{*}$ and $B\to KJ/\psi {\pi }^{+}{\pi }^{-}$ decay processes. The competition between the rescattering mediated through a Breit-Wigner resonance and the rescattering generated from a local $D{\overline{D}}^{*}\to D{\overline{D}}^{*}$ interaction is carefully studied through an effective Lagrangian approach. Three different fits are performed: pure Breit-Wigner case, pure $D{\overline{D}}^{*}$ molecule case with only local rescattering vertices (generated by the loop chain), and the mixed case. It is found that data supports the picture where $X(3872)$ is mainly a ($\overline{c}c$) Breit-Wigner resonance with a small contribution to the self-energy generated by $\overline{D}{D}^{*}$ final state interaction. For our optimal fit, the pole mass and width are found to be: $M_X=3871.2\pm 0.7\mathrm{MeV}$ and ${\mathrm{\Gamma }}_X=6.5\pm 1.2\mathrm{MeV}$.

A possible manifestation of an additional light gauge boson $A^{\prime }$, named a dark photon, associated with a group $U(1{)}_{\mathrm{B}-\mathrm{L}}$, is studied in neutrino-electron scattering experiments. The exclusion plot on the coupling constant $g_{\mathrm{B}-\mathrm{L}}$ and the dark photon mass $M_{A^{\prime }}$ is obtained. It is shown that the contributions of interference terms between the dark photon and the Standard Model are important. The interference effects are studied and compared with data sets from TEXONO, GEMMA, BOREXINO, and LSND, as well as CHARM II experiments. Our results provide more stringent bounds to some regions of parameter space.

Within the framework of holography applied to condensed matter physics, we study a model of perturbatively charged disorder in $D=4$ dimensions. Starting from initially uncharged ${\mathrm{AdS}}_4$, a randomly fluctuating boundary chemical potential is introduced by turning on a bulk gauge field parametrized by a disorder strength $\overline{V}$ and a characteristic scale $k_0$. Accounting for gravitational backreaction, we construct an asymptotically anti–de Sitter (AdS) solution perturbatively in the disorder strength. The disorder averaged geometry displays unphysical divergences in the deep interior. We explain how to remove these divergences and arrive at a well behaved solution. The disorder averaged dc conductivity is calculated and is found to contain a correction to the AdS result. The correction appears at second order in the disorder strength and scales inversely with $k_0$. We discuss the extension to a system with a finite initial charge density. The disorder averaged dc conductivity may be calculated by adopting a technique developed for holographic lattices.

We investigate some aspects of Bogomolny-Prasad-Sommerfield monopole solutions in the Yang-Mills-Higgs theory with the exceptional gauge group $G_2$ spontaneously broken to $U(1)\times U(1)$. The corresponding homotopy group is ${\pi }_2(G_2/U(1)\times U(1))$, and similarly to the $SU(3)$ theory, the $G_2$ monopoles are classified by two topological charges $(n_1,n_2)$. In the fundamental representation, these yield a subset of $SO(7)$ monopole configurations. Through inspection of the structure of $Alg(G_2)$, we propose an extension of the Nahm construction to the $(n,1{)}_{G_2}$ monopoles. For the $(1,1{)}_{G_2}$ monopole, the Nahm data are written explicitly.