Space-time Directions Research Articles

Lorentz violation in γ-pair production (e + e − → γ γ)

In this paper, we investigate the production process of a photon pair in a regime of quantum electrodynamics, considering the presence of a constant four-vector that defines a privileged direction in spacetime, resulting in Lorentz symmetry violation. We explore Lorentz violation in the context of vectorial nonminimal coupling, where we analyze the modifications introduced by this coupling in the scattering amplitude at the vertex. Moreover, we delve into Lorentz violation with axial-like nonminimal coupling. Both analyses are conducted by examining the constant four-vector of both time-like and space-like types.

Loop correction to the scalar Casimir energy density and generation of topological mass due to a helix boundary condition in a scenario with Lorentz violation

In this paper, the effective potential approach in quantum field theory is used in order to investigate self-interaction loop correction to the Casimir energy density and generation of topological mass for both massless and massive real scalar fields. It is assumed that the scalar field obeys a helix boundary condition. In addition, it is also considered a CPT-even aether-type violation of the Lorentz symmetry. In the absence of the Lorentz violation, we obtain analytical expressions for the loop correction to the Casimir energy density and to the mass of the scalar field. The same expressions are also obtained assuming the Lorentz violation in each of the spacetime directions. We also show some graphs that exhibit how the loop correction and the Lorentz violation affect the Casimir energy density and the mass of the scalar field.

Fast structure-preserving difference algorithm for 2D nonlinear space-fractional wave models

In this article, we present an efficient structure-preserving difference scheme for two-dimensional nonlinear space fractional wave models. We use the Crank-Nicolson scheme to discretize in the time direction, and adopt a shifted convolution quadrature (SCQ) formula to approximate the spatial direction. We show and prove an important lemma, and then based on this lemma, we rigorously derive the energy dissipation for the damped case and the approximate energy conservation in undamped case for the fully discrete scheme. In addition, we do the detailed analysis for error estimates with the optimal convergence result O ( h x 2 + h y 2 + τ 2 ) , where h x , h y and τ denote the step length in space-time directions. Furthermore, we provide an efficient fast algorithm called the preconditioned fast BiCG (PF-BiCG) to reduce the cost of time and save memory. Finally, we carry out numerical tests by taking three numerical examples to validate the theories, to observe the performance behaviors of wave solutions, and to reveal the relationship between models by changing fractional parameters.

Decay properties of N(1535) in the holographic QCD

We study one pion emission decay of the first excited state of the nucleon with negative parity $N(1535) \equiv N^*$ in the holographic model of QCD. The excited state is described as a vibrational mode along the extra $z$ direction in the five-dimensional space-time of the model. We have obtained an analytic formula for the axial coupling of $g_A^{NN^*}$. The off-diagonal axial coupling is obtained at the decaying pion momentum $|\boldsymbol{k}| = 448$ MeV as $g_A^{NN^*} \sim 0.32$, and hence a partial decay width $\Gamma_{N^* \to \pi N} \sim 30$ MeV, which is smaller than but reasonably compared to the experimental data.

Mathematical foundations for field theories on Finsler spacetimes

This paper introduces a general mathematical framework for action-based field theories on Finsler spacetimes. As most often fields on Finsler spacetime (e.g., the Finsler fundamental function or the resulting metric tensor) have a homogeneous dependence on the tangent directions of spacetime, we construct the appropriate configuration bundles whose sections are such homogeneous fields; on these configuration bundles, the tools of coordinate free calculus of variations can be consistently applied to obtain field equations. Moreover, we prove that the general covariance of natural Finsler field Lagrangians leads to an averaged energy–momentum conservation law that, in the particular case of Lorentzian spacetimes, is equivalent to the usual pointwise energy–momentum covariant conservation law.

The near-horizon geometry of supersymmetric rotating AdS4 black holes in M-theory

We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity which are associated to rotating M2-branes. Such rotating black holes admit an AdS2 near-horizon geometry which is fibered by the transverse spacetime directions. In this paper we allow for the most general fibration over AdS2 with a flux configuration permitting rotating M2-branes. Using G-structure techniques we rewrite the conditions for supersymmetry in terms of differential equations on an eight-dimensional balanced space. The 9d compact internal space is a U(1)-fibration over this 8d base. The geometry is constrained by a master equation reminiscent of the one found in the non-rotating case. We give a Lagrangian from which the equations of motion may be derived, and show how the asymptotically AdS4 electrically charged Kerr-Newman black hole in 4d mathcal{N} = 2 supergravity is embedded in the classification. In addition, we present the conditions for the near-horizon geometry of rotating black strings in Type IIB by using dualities with the 11d setup.

Scattering in strong electromagnetic fields: Transverse size effects in time-dependent basis light-front quantization

The framework of 'time-dependent basis light-front quantisation' (tBLFQ) offers a non-perturbative approach to scattering problems in external fields, based on Fock space truncation. Here we extend tBLFQ to include spatio-temporal field inhomogeneities in multiple spacetime directions. This extension is necessary for the proper modelling of e.g. intense laser fields. We focus on the example of nonlinear Compton scattering of an electron on an axicon-type laser, with an emphasis on the transverse structure of the beam. We analyse the impact of field intensity and particle energy, as well as basis truncation effects, on the radiation spectrum of the scattered electron.

Directional massive gravity

We propose a new model of Lorentz breaking massive gravity in which the mass of the graviton depends from the space-time directions. We explore its consistency: absence of ghosts, tachyons, gradient instabilities, VDVZ discontinuities. We demonstrate that the model is not plagued by any pathology in a large region of parameters space. Within this new theory, we find several interesting phenomena. First of all, gravitational waves propagate an-isotropically in space-time. Second, we find anisotropic corrections to the Newtonian potential, with new extra Yukawa-like phases. Such a scenario also carries intriguing consequences in context of large extra dimensions proposals, as a confinement mechanism of gravity in [Formula: see text] dimensions.

Intermediate scalings for solv, nil, and SL2(R) black branes

In this work we will study black brane solutions that are not translationally invariant in the spatial directions along which it extends. Instead, we require homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. We find Einstein-Maxwell black hole solutions whose near horizon geometry correspond to Solv (Bianchi $V1_{-1}$), Nil (Bianchi $II$) or $SL_2({\cal R})$ (Bianchi $VIII$). Interestingly we observe that at intermediate temperatures our solutions have an scaling regime where different spacetime directions scale differently. We also compute the DC conductivities for these charged solutions and study how they scale in this intermediate regime.

Abelian 1-Form Gauge Theory in Very Special Relativity

We study an Abelian 1-form gauge theory in the context of very special relativity. The very special relativity regards subgroup of Lorentz group as fundamental symmetry of the nature than the full Lorentz group. The rotational symmetry of the Lorentz symmetry breaks down by chosing a privileged direction in spacetime. We discuss the BRST invariant and anti-BRST invariant superspace formulations for such BV actions. The VSR modified BRST invariant BV action corresponding to the Abelian 1-form gauge theory can be written manifestly covariant manner in a superspace with one Grassmann coordinate. Moreover, we can write down the the VSR modified extended BRST and extended anti-BRST invariant BV actions in a superspace with two Grassmann coordinates. The results thus obtained is in complete agreement with the Lorentz invariant theory.

Lagrangian formulation and symmetrical description of liquid dynamics.

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.

Phenomenological implications of very special relativity

We discuss several phenomenological implications of Very Special Relativity (VSR). It is assumed that there is a small violation of Lorentz invariance and the true symmetry group of nature is a subgroup called SIM(2). This symmetry group postulates the existence of a fundamental or preferred direction in space-time. We study its implications by using an effective action which violates Lorentz invariance but respects VSR. We find that the problem of finding the masses of fundamental fermions is in general intractable in the presence of VSR term. The problem can be solved only in special cases which we pursue in this paper. We next determine the signal of VSR in torsion pendulum experiment as well as clock comparison experiment. We find that VSR predicts a signal which is different from other Lorentz violating theories and hence a dedicated data analysis is needed in order to impose reliable limits. Assuming that signal is absent in data we determine the limits that can be imposed on the VSR parameters. We also study the implications of VSR in particle decay experiments taking the charged pion and kaon decay as an example. The effective interaction between the charged pion and the final state leptons is related to the fundamental VSR mass terms through a loop calculation. We also predict a shift in the angular dependence of the decay products due to VSR. In particular we find that these no longer display azimuthal symmetry with respect to the momentum of the pion. Furthermore the azimuthal and polar angle distributions show time dependence with a period of a sidereal day. This time dependence provides us with a novel method to test VSR in future experiments.

Fermionic Lorentz violation and its implications for interferometric gravitational-wave detection

The recent direct detection of gravitational waves reported by Advanced LIGO has inspired the current article. In this context, a particular Lorentz-violating framework for classical, massive particles is the focus. The latter is characterized by a preferred direction in spacetime comprised of CPT-odd components with mass dimension 1. Curvature effects in spacetime, which are caused by a propagating gravitational wave, are assumed to deform the otherwise constant background field. In accordance with spontaneous Lorentz violation, a particular choice for the vector field is taken, which was proposed elsewhere. The geodesic equations for a particle that is subject to this type of Lorentz violation are obtained. Subsequently, their numerical solutions are computed and discussed. The particular model considered leads to changes in the particle trajectory whose impact on interferometric gravitational-wave experiments such as LIGO will be studied.

Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

In this paper, we study theoretically atomic quantum simulations of a U(1) gauge-Higgs model on a three-dimensional (3D) spatial lattice by using an extended Bose-Hubbard model with intersite repulsions on a 3D optical lattice. Here, the phase and density fluctuations of the boson variable on each site of the optical lattice describe the vector potential and the electric field on each link of the gauge-model lattice, respectively. The target gauge model is different from the standard Wilson-type U(1) gauge-Higgs model because it has plaquette and Higgs interactions with asymmetric couplings in the space-time directions. Nevertheless, the corresponding quantum simulation is still important as it provides us with a platform to study unexplored time-dependent phenomena characteristic of each phase in the general gauge-Higgs models. To determine the phase diagram of the gauge-Higgs model at zero temperature, we perform Monte-Carlo simulations of the corresponding 3+1-dimensional U(1) gauge-Higgs model, and obtain the confinement and Higgs phases. To investigate the dynamical properties of the gauge-Higgs model, we apply the Gross-Pitaevskii equations to the extended Bose-Hubbard model. We simulate the time-evolution of an electric flux that initially is put on a straight line connecting two external point charges. We also calculate the potential energy between this pair of charges and obtain the string tension in the confinement phase. Finally, we propose a feasible experimental setup for the atomic simulations of this quantum gauge-Higgs model on the 3D optical lattice. These results may serve as theoretical guides for future experiments.

Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymer

We consider the Beta polymer, an exactly solvable model of directed polymer on the square lattice, introduced by Barraquand and Corwin (BC) (2016 Probab. Theory Relat. Fields 1–16). We study the statistical properties of its point to point partition sum. The problem is equivalent to a model of a random walk in a time-dependent (and in general biased) 1D random environment. In this formulation, we study the sample to sample fluctuations of the transition probability distribution function (PDF) of the random walk. Using the Bethe ansatz we obtain exact formulas for the integer moments, and Fredholm determinant formulas for the Laplace transform of the directed polymer partition sum/random walk transition probability. The asymptotic analysis of these formulas at large time t is performed both (i) in a diffusive vicinity, , of the optimal direction (in space-time) chosen by the random walk, where the fluctuations of the PDF are found to be Gamma distributed; (ii) in the large deviations regime, , of the random walk, where the fluctuations of the logarithm of the PDF are found to grow with time as t1/3 and to be distributed according to the Tracy–Widom GUE distribution. Our exact results complement those of BC for the cumulative distribution function of the random walk in regime (ii), and in regime (i) they unveil a novel fluctuation behavior. We also discuss the crossover regime between (i) and (ii), identified as . Our results are confronted to extensive numerical simulations of the model.

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory.

We demonstrate that, for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent timelike direction in dS spacetime is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher-spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS spacetime.

Quaternionic quantization principle in general relativity and supergravity

A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space–time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism, the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to [Formula: see text] supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.

The field theories construction in spacetime with deformed Poincaré subgroups symmetries

The modern experiments have put strict restrictions on the possible violation of local Lorentz and CPT invariance. However there seem to exist some clues showing that the two symmetries are possibly broken. It would be remarkable to find out the possible breaking mechanism and build up a reasonable framework with Lorentz or CPT violation. As the spacetime corresponding to all possible of deformation of all the Poincare subgroups of the forms of semi product of the Lorentz subgroup with the spacetime translation are almost of Finsler type. We study here the particle dynamics in these Finsler spacetime and investigate their dispersion relations based on which we investigate the possible self-consistent field theories dynamics in the Finsler spacetime including scalar field, spinor field, vector field and gauge coupling. The modifications caused by deformation relative to field theories in Minkowski spacetime are discussed. The Finsler structures we study in this paper have strong dependence on the space-time direction. Thus, if space-time is of Finsler type, we can observe the dependence by well designed experiment.

O(D, D) covariant Noether currents and global charges in double field theory

Double field theory is an approach for massless modes of string theory, unifying and geometrizing all gauge invariance in manifest $\mathbf{O}(D,D)$ covariant manner. In this approach, we derive off-shell conserved Noether current and corresponding Noether potential associated with unified gauge invariance. We add Wald-type counter two-form to the Noether potential and define conserved global charges as surface integral. We check our $\mathbf{O}(D,D)$ covariant formula against various string backgrounds, both geometric and non-geometric. In all cases we examined, we find perfect agreements with previous results. Our formula facilitates to evaluate momenta along not only ordinary spacetime directions but also dual spacetime directions on equal footing. From this, we confirm recent assertion that null wave in doubled spacetime is the same as macroscopic fundamental string in ordinary spacetime.

Dynamics of cosmic strings with higher-dimensional windings

We consider F-strings with arbitrary configurations in the Minkowski directions of a higher-dimensional spacetime, which also wrap and spin around S1 subcycles of constant radius in an arbitrary internal manifold, and determine the relation between the higher-dimensional and the effective four-dimensional quantities that govern the string dynamics. We show that, for any such configuration, the motion of the windings in the compact space may render the string effectively tensionless from a four-dimensional perspective, so that it remains static with respect to the large dimensions. Such a critical configuration occurs when (locally) exactly half the square of the string length lies in the large dimensions and half lies in the compact space. The critical solution is then seen to arise as a special case, in which the wavelength of the windings is equal to their circumference. As examples, long straight strings and circular loops are considered in detail, and the solutions to the equations of motion that satisfy the tensionless condition are presented. These solutions are then generalized to planar loops and arbitrary three-dimensional configurations. Under the process of dimensional reduction, in which higher-dimensional motion is equivalent to an effective worldsheet current (giving rise to a conserved charge), this phenomenon may be seen as the analogue of the tensionless condition which arises for superconducting and chiral-current carrying cosmic strings.