Lorentz Invariance Research Articles

Discrete gravity with local Lorentz invariance

A novel structure-preserving algorithm for general relativity in vacuum is derived from a lattice gauge theoretic discretization of the tetradic Palatini action. The resulting model of discrete gravity is demonstrated to preserve local Lorentz invariance and symplectic structure.

Induced Yang-Mills-Non-Abelian-Chern-Simons action in three dimensions

In this paper, we consider the massive quarks interacting with an external non-abelian gauge field (gluon) in (1+2)-dimensional spacetime. By integrating out the quark fields, we obtain the general structure of the one-loop effective action for the gluons coupled to the quarks. Next, we compute the one-loop Feynman graphs related to one, two, three and four-point functions for the gluon, by using dimensional regularization. We explicitly show that the resulting effective action, at the low-energy limit (), leads to the non-Abelian Chern-Simons and Yang-Mills action. This induced action, arising from the quantum corrections due to the fermionic loops, also respects Lorentz and gauge invariance.

Energy extraction via magnetic reconnection in Lorentz breaking Kerr–Sen and Kiselev black holes

Black holes can accumulate a large amount of energy, responsible for highly energetic astrophysical phenomena. Although the Blandford–Znajek is considered to date the leading mechanism for powering jets and GRBs, recently fast magnetic reconnection (MR) of the magnetic field was proposed as a new way to extract energy. In this paper, we investigate this phenomena in a bumblebee Kerr–Sen BH, which differentiates from standard Kerr solution via a Lorentz symmetry breaking parameter ell and an electric charge one b. We find that the presence of the charge parameter strongly changes the simple Kerr case, making this extraction mechanism possible even for not extremely rotating black holes (asim 0.7). We also show that, under appropriate circumstances, MR is more efficient compared to the Blandford–Znajek mechanism. We finally compare these results with dark energy (quintessence) black-hole solutions. In this case, we find that a Kerr black hole is indistinguishable from a rotational Kiselev one, whatever the energy-matter that surrounds it (including ordinary matter, such as dust and radiation).

The Casimir Energy for Lorentz-Violating Scalar Field in Sphere

Abstract: In the present article, the Casimir energy was computed for the massless and Lorentz-violating scalar field, confined in a sphere with Dirichlet and Neumann boundary conditions. In 3+1 space-time dimensions, four violated directions to break the Lorentz symmetry are likely, according to which we presented the Casimir energy regarding all possible directions for the Lorentz violation and discussed the pure contribution to the Lorentz violation in a language of graphs. In the details of the calculation, a simple method was developed based on the direct mode summation and the sum-over-modes were performed via the contour integration in a complex plane of eigenfrequencies. The obtained result for all cases of Lorentz symmetry breaking was consistent with the expected physical basis. Keywords: Casimir energy, Lorentz-violating sphere scalar field. PACS No: 11.10.z; 11.10.Gh; 11.25.Db; 11.15.Bt

“The more things change the more they stay the same” Minimum lengths with unmodified uncertainty principle and dispersion relation

Broad arguments indicate that quantum gravity should have a minimal length scale. In this paper, we construct a minimum length model by generalizing the time-position and energy–momentum operators while keeping much of the structure of quantum mechanics and relativity intact: the standard position-momentum commutator, the special relativistic time-position, and energy–momentum relationships all remain the same. Since the time-position and energy–momentum relationships for the modified operators remain the same, we retain a form of Lorentz symmetry. This avoids the constraints on these theories coming from lack of photon dispersion while holding the potential to address the Greisen–Zatsepin–Kuzmin (GZK) puzzle of ultra high-energy cosmic rays.

Crystal gravity

We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space itself. Only rather recently it was realized in various context that the order parameter of the solid has a relation to Einsteins dynamical space time which is similar to the role of a Higgs field in a Yang-Mills gauge theory. Such a "crystal gravity" is therefore like the Higgs phase of gravity. The usual Higgs phases are characterized by a special phenomenology. A case in point is superconductivity exhibiting phenomena like the Type II phase, characterized by the emergence of an Abrikosov lattice of quantized magnetic fluxes absorbing the external magnetic field. What to expect in the gravitational setting? The theory of elasticity is the universal effective field theory associated with the breaking of space translations and rotations having a similar status as the phase action describing a neutral superfluid. A geometrical formulation appeared in its long history, similar in structure to general relativity, which greatly facilitates the marriage of both theories. With as main limitation that we focus entirely on stationary circumstances -- the dynamical theory is greatly complicated by the lack of Lorentz invariance -- we will present a first exploration of a remarkably rich and often simple physics of "Higgsed gravity".

Field Theory of Interacting Boundary Gravitons

Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by GG and \LambdaΛ. As a consequence, correlation functions of the boundary stress tensor in AdS_33 are uniquely fixed in terms of one dimensionless parameter, which is the central charge of the Virasoro algebra. The same argument implies that AdS_33 gravity at a finite radial cutoff is a renormalizable theory, but now with one additional parameter corresponding to the cutoff location. This theory is conjecturally dual to a T\overline{T}TT¯-deformed CFT, assuming that such theories actually exist. To elucidate this, we study the quantum theory of boundary gravitons living on a cutoff planar boundary and the associated correlation functions of the boundary stress tensor. We compute stress tensor correlation functions to two-loop order (GG being the loop counting parameter), extending existing tree level results. This is made feasible by the fact that the boundary graviton action simplifies greatly upon making a judicious field redefinition, turning into the Nambu-Goto action. After imposing Lorentz invariance, the correlators at this order are found to be unambiguous up to a single undetermined renormalization parameter.

Supersymmetric action for 6D (4, 0) supergravity

We give a linearized but otherwise complete supersymmetric action for mathcal{N} = (4, 0) supergravity in six dimensions, using a Kaluza-Klein-type 5 + 1 split of coordinates and fields. We provide in particular a significantly simplified version of the bosonic action derived by us recently. This formulation employs fields that are no longer irreducible, subject to a local Lorentz invariance, which in turn simplifies the supersymmetry transfor mations including the exotic gravitino.

Ultra-High-Energy Astroparticles as Probes for Lorentz Invariance Violation

Compelling evidence for Lorentz invariance violation (LIV) would demand a complete revision of modern physics. Therefore, searching for a signal or extending the validity of the invariance is fundamental for building our understanding of the extreme phenomena in the Universe. In this paper, we review the potential of ultra-high-energy astroparticles in setting limits on LIV. The standard framework of LIV studies in astroparticle physics is reviewed and its use on the electromagnetic and hadronic sectors are discussed. In particular, the current status of LIV tests using experimental data on ultra-high-energy photons and cosmic rays is addressed. A detailed discussion with improved argumentation about the LIV kinematics of the relevant interactions is shown. The main previous results are presented together with new calculations based on recently published astrophysical models.

Modification method of NUT-Kerr-Newman-de Sitter black hole entropy by Lorentz symmetry breaking and beyond the semi-classical approximation

According to Lorentz symmetry breaking and black hole quantum tunneling radiation theory, aether-like field is correctly introduced into the general stationary black hole space-time, and the modified boson dynamic equation is obtained. On this basis, the Hawking temperature and black hole entropy of NUT-Kerr-Newman-de Sitter black hole with general stationary characteristics are modified, and the method used in this paper and the significance of the conclusions are deeply discussed.

An improvement for quantum tunneling radiation of fermions in the Kerr–Newman black hole

By introducing a specific aether-like vector in the Dirac equation with Lorentz Invariance Violation (LIV) in the curved spacetime, an improved method for quantum tunneling radiation of fermions is proposed. As an example, we apply this new method to the horizons of a stationary charged axisymmetric Kerr–Newman black hole. Considering LIV theory, we firstly obtain a modified dynamical equation for fermions with spin 12 in the Kerr–Newman spacetime and then solve the equation. We find the increase or decrease of both the Hawking temperature and entropy are related to constants a and c in the modified Dirac equation. The new Hawking temperature is about 1+2a+2cmkr21+2a times higher than that in the fiducial calculation, but the entropy will decrease. In this case, the evaporation of the black hole will be accelerated. We also make a brief discussion for the case of fermions with high spin.

The origin of Weyl gauging in metric-affine theories

In the first part, we discuss the interplay between local scale invariance and metric-affine degrees of freedom from few distinct points of view. We argue, rather generally, that the gauging of Weyl symmetry is a natural byproduct of requiring that scale invariance is a symmetry of a gravitational theory that is based on a metric and on an independent affine structure degrees of freedom. In the second part, we compute the Nöther identities associated with all the gauge symmetries, including Weyl, Lorentz and diffeomorphisms invariances, for general actions with matter degrees of freedom, exploiting a gauge covariant generalization of the Lie derivative. We find two equivalent ways to approach the problem, based on how we regard the spin-connection degrees of freedom, either as an independent object or as the sum of two Weyl invariant terms. The latter approach, which rests upon the use of a Weyl-covariant connection with desirable properties, denoted , is particularly convenient and constitutes one of our main results.

Probing bumblebee gravity with black hole X-ray data

Bumblebee gravity is one of the simplest gravity theories with spontaneous Lorentz symmetry breaking. Since we know a rotating black hole solution in bumblebee gravity, we can potentially test this model with the available astrophysical observations of black holes. In this work, we construct a reflection model in bumblebee gravity and we use our model to analyze the reflection features of a NuSTAR spectrum of the Galactic black hole EXO 1846-031 in order to constrain the Lorentz-violating parameter ell . We find that the analysis of the reflection features in the spectrum of EXO 1846-031 cannot constrain the parameter ell because of a very strong degeneracy between the estimates of ell and of the black hole spin parameter a_*. Such a degeneracy may be broken by combining other observations.

Massive Quarks at One Loop in the Dipole Picture of Deep Inelastic Scattering.

We calculate the light cone wave functions for a virtual photon to split into quark-antiquark states, including for the first time quark masses at one loop accuracy. These wave functions can be used to calculate cross sections for several precision probes of perturbative gluon saturation at the Electron-Ion Collider. Using these wave functions we derive, for the first time, the dipole picture deep inelastic scattering cross sections at one loop for longitudinal and transverse virtual photons including quark masses. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance of the quark Dirac and Pauli form factors.

Massive quarks in NLO dipole factorization for DIS: Transverse photon

We calculate the light cone wave functions for the QCD Fock components in a transverse virtual photon necessary for applications at next-to-leading order in the QCD coupling, including quark masses. We present a detailed calculation of both the one loop wave function for the quark-antiquark Fock component and the tree level wave function for the quark-antiquark-gluon Fock component. The quark masses are renormalized in the pole mass scheme, satisfying constraints from the requirement of Lorentz invariance. In particular the quark Pauli form factor at NLO is recovered from the on-shell limit of the quark-antiquark Fock component. We use our result to calculate the next-to-leading order correction to the high energy deep inelastic scattering (DIS) transverse structure function on a dense target in the dipole factorization framework. Together with our earlier result for longitudinal photons, this completes the calculation of the total deep inelastic scattering cross section in the dipole picture with massive quarks at next-to-leading order, enabling a comparison with experimental data.

Entanglement wedge minimum cross-section for holographic aether gravity

We study the entanglement wedge cross-section (EWCS) in holographic Aether gravity theory, a gravity theory with Lorentz symmetry violation while keeping the general covariance intact. We find that only a limited parameter space is allowed to obtain a black brane with positive Hawking temperature. Subject to these allowed parameter regions, we find that the EWCS could exhibit non-monotonic behaviors with system parameters. Meanwhile, the holographic entanglement entropy (HEE), and the corresponding mutual information (MI), can only exhibit monotonic behaviors. These phenomena suggest that the EWCS could capture much more rich content of the entanglement than that of the HEE and the MI. The role of the Lorentz violation in determining the behaviors of quantum information-related quantities is also analyzed.

Harmonic-type central potential effects induced by Lorentz symmetry violation on relativistic quantum oscillator field

Harmonic-type central potential effects induced by Lorentz symmetry violation on relativistic quantum oscillator field

Renormalization scheme dependence of beta -functions in Lorentz-violating quantum field theory

Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa theory show that when this kind of redundancy exists, different renormalization schemes may lead to different expressions for the renormalization group beta -functions, even at only one-loop order. However, the renormalization group scaling of physically observable quantities appears not to share this kind of scheme dependence.

Spectral Lag Transition of 32 Fermi Gamma-Ray Bursts and Their Application on Constraining Lorentz Invariance Violation

The positive-to-negative transition of spectral lag is an uncommon feature reported in a small number of gamma-ray bursts (GRBs). An application of such a feature has been made to constrain the critical quantum gravity energy (E QG) of the light photons under the hypothesis that the Lorentz invariance might be violated. Motivated by previous case studies, this paper systematically examined the up-to-date GRB sample observed by Fermi Gamma-ray Burst Monitor for the lag transition feature to establish a comprehensive physical limit on the Lorentz invariance violation (LIV). This search resulted in 32 GRBs with redshift available, which exhibit the lag transition phenomenon. We first fit each of the lag–E relations of the 32 GRBs with an empirical smoothly broken power-law function, and found that the lag transition occurs typically at about 400 keV. We then implemented the LIV effect into the fit, which enabled us to constrain the lower limit of the linear and quadratic values of E QG, which are typically distributed at 1.5 × 1014 and 8 × 105 GeV, respectively.

Generalized quantum oscillator under harmonic-type central potential effects induced by Lorentz symmetry violation environment(a)

In this paper, we study a relativistic quantum oscillator model via the generalized Klein-Gordon oscillator equation under harmonic-type central potential effects induced by the violation of the Lorentz symmetry. We determine solutions of the wave equation for Coulomb- and Cornell-type potential functions using the Nikiforov-Uvarov method and analyze the effects on the energy profile and the wave function of the oscillator fields.