International Journal of Modern Physics A

The turbulence in incompressible fluid is represented as a field theory in 3 dimensions. There is no time involved, so this is intended to describe stationary limit of the Hopf functional. The basic fields are Clebsch variables defined modulo gauge transformations (symplectomorphisms). Explicit formulas for gauge invariant Clebsch measure in space of generalized Beltrami flow compatible with steady energy flow are presented. We introduce a concept of Clebsch confinement related to unbroken gauge invariance and study Clebsch instantons: singular vorticity sheets with nontrivial helicity. This is realization of the “instantons and intermittency” program we started back in the 1990s.¹ These singular solutions are involved in enhancing infinitesimal random forces at remote boundary leading to critical phenomena. In the Euler equation vorticity is concentrated along the random self-avoiding surface, with tangent components proportional to the delta function of normal distance. Viscosity in Navier–Stokes equation smears this delta function to the Gaussian with width $h\propto {\nu }^{3/5}$ at $\nu \to 0$ with fixed energy flow. These instantons dominate the enstrophy in dissipation as well as the PDF for velocity circulation ${\mathrm{\Gamma }}_C$ around fixed loop $C$ in space. At large loops, the resulting symmetric exponential distribution perfectly fits the numerical simulations² including pre-exponential factor $1/\sqrt{\left|\mathrm{\Gamma }\right|}$. At small loops, we advocate relation of resulting random self-avoiding surface theory with multi-fractal scaling laws observed in numerical simulations. These laws are explained as a result of fluctuating internal metric (Liouville field). The curve of anomalous dimensions $\zeta (n)$ can be fitted at small $n$ to the parabola, coming from the Liouville theory with two parameters $\alpha$, $Q$. At large $n$ the ratios of the subsequent moments in our theory grow linearly with the size of the loop, which corresponds to finite value of $\zeta (\infty )$ in agreement with DNS.

The inert Zee model is an extension of the Zee model for neutrino masses. This new model explains the dark matter relic abundance, generates a one-loop neutrino masses and forbids tree-level Higgs-mediated flavor changing neutral currents. Although the dark matter phenomenology of the model is similar to that of the inert doublet model, the presence of new vector-like fermions opens the lepton portal as a new dark matter annihilation channel. We study the impact of this new portal in the low-mass regime and show the parameter space allowed by direct and indirect searches of dark matter. Remarkably, the region for $m_{H^0}\lesssim 70$ GeV is recovered for ${\lambda }_L\lesssim 10^{-3}$. We also show that future experiments like LZ and DARWIN could probe a large region of the parameter space of the model.

In this paper, we construct super fuzzy Dirac and chirality operators on the super fuzzy Euclidean hyperboloid ${\mathrm{\text{EAdS}}}_F^{(2|2)}$ in-instanton and no-instanton sectors. Using the super pseudo-projectors of the noncompact first Hopf fibration, we construct the Ginsparg–Wilson algebra in instanton and no-instanton sectors. Then, using the generators of this algebra, we construct pseudo super-Dirac and chirality operators in both sectors. We also construct pseudo super-Dirac and chirality operators corresponding to the case in which our theory includes gauge fields. We show that they have correct commutative limit in the limit case when the noncommutative parameter $l$ tends to infinity.

We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coefficients of the power series that, under suitable truncation, yields exact analytical eigenvalues and eigenfunctions for particular values of a model parameter. From these solutions some researchers have derived a variety of predictions like allowed angular frequencies, allowed field intensities and the like. We also solve the eigenvalue equation numerically by means of the variational Ritz method and compare the resulting eigenvalues with those provided by the truncation condition. In this way we prove that those physical predictions are merely artifacts of the truncation condition.

We show that a Reissner–Nordström (RN) black hole can be formed by dropping a charged thin dust shell onto a RN naked singularity. This is in contrast to the fact that a RN naked singularity is prohibited from forming by dropping a charged thin dust shell onto a RN black hole. This implies the strong tendency of the RN singularity to be covered by a horizon in favor of cosmic censorship. We show that an extreme RN black hole can also be formed from a RN naked singularity by the same process in a finite advanced time. We also discuss the evolution of the charged thin dust shells and the causal structure of the resultant space–times.

Here we propose the extended modified gravity theory named $f(R,G,{𝒯})$ gravity where $R$ is the Ricci scalar, $G$ is the Gauss–Bonnet invariant, and ${𝒯}$ is the trace of the stress-energy tensor. We derive the gravitational field equations in $f(R,G,{𝒯})$ gravity by taking the least action principle. Next we construct the $f(R,G,{𝒯})$ in terms of $R$, $G$ and ${𝒯}$ in de Sitter as well as power-law expansion. We also construct $f(R,G,{𝒯})$ if the expansion follows the finite-time future singularity (big rip singularity). We investigate the energy conditions in this modified theory of gravity and examine the validity of all energy conditions.

Creation of charged massless fermion pair by a photon in a constant uniform magnetic field is considered in the one-loop approximation of the $(2+1)$-dimensional quantum electrodynamics (QED${}_{2+1}$). We calculate the elastic scattering amplitude (EAS) of photon using the polarization operator of photon in the above magnetic field obtained earlier in our work. We analyze the elastic scattering amplitude of photon at various values of the photon energy and magnetic field strength. Very simple analytical formulas for EAS of photon are obtained in the so-called quasi-classical region. In the massive quantum electrodynamics the elastic scattering amplitude of photon defines its “mass” squared in the presence of external electromagnetic field and the imaginary part of EAS describes the total probability of charged massive fermion pair creation in the electromagnetic field; we assume that it is the case and in the massless quantum electrodynamics.

A Satellite Fermi GBM detected recent putative short Gamma Ray Bursts (GRBs) in coincident with the gravitational wave signal GW 150914 produced by the merger of binary black hole (BH). If at least one BH possess magnetic monopole charge in the binary BH system then the short-duration GRBs may produce during the final phase of a binary BH merger. The detection of gravitational waves GW 150914, GW 151226 and LVT 151012 by LIGO gave the evidence that merging of the compact object like binary BH often happens in our universe. In this paper, we report the qualitative model to discuss the generation of electromagnetic radiation from the merging of two BHs with equal masses and at least one BH carrying the magnetic monopole charge in the binary system. In this model, BH possess a magnetic monopole charge that may not be neutralized before the coalescence. During the inspiralling process, the magnetic monopole charge on the BH would produced the electric dipole moment. Short duration GRB would produce by the rapidly evolution of the electric dipole moment which may detectable on Earth. We predict that this model would be beneficial in the future to explain the generation of gravitational wave (GW) plus a electromagnetic signal of multi-wavelength from mergers of magnetically charged BHs.

We study diagonal representatives of boundary condition matrices on the orbifolds $S^1/Z_2$ and $T^2/Z_m$ $(m=2,3,4,6)$. We give an alternative proof of the existence of diagonal representatives in each equivalent class of boundary condition matrices on $S^1/Z_2$, using a matrix exponential representation, and show that they do not necessarily exist on $T^2/Z_2$, $T^2/Z_3$, and $T^2/Z_4$. Each equivalence class on $T^2/Z_6$ has a diagonal representative, because its boundary conditions are determined by a single unitary matrix.

In this paper, I study the Casimir effect caused by a charged and massive scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner. I investigate the case of a scalar field that satisfies Dirichlet or mixed (Dirichlet–Neumann) boundary conditions on a pair of very large plane parallel plates. The case of Neumann boundary conditions is straightforward and will not be examined in detail. I use the $\zeta$-function regularization technique to study the effect of a constant magnetic field, orthogonal to the plates, on the Casimir energy and pressure. I investigate the cases of a timelike Lorentz asymmetry, a spacelike Lorentz asymmetry in the direction perpendicular to the plates, and a spacelike asymmetry in the plane of the plates and, in all those cases, derive simple analytic expressions for the zeta function, Casimir energy and pressure in the limits of small plate distance, strong magnetic field and large scalar field mass. I discover that the Casimir energy and pressure, and their magnetic corrections, all strongly depend on the direction of the unit vector that implements the breaking of the Lorentz symmetry.