Breaking Of Lorentz Invariance Research Articles

Fermion self-energy and effective mass in a noisy magnetic background

In this article, we consider the propagation of QED fermions in the presence of a classical background magnetic field with white-noise stochastic fluctuations. The effects of the magnetic field fluctuations are incorporated into the fermion and photon propagators in a quasiparticle picture, which we developed in previous works using the . By working in the very strong-field limit, here we explicitly calculate the fermion self-energy involving radiative contributions at first order in αem, in order to obtain the noise-averaged mass of the fermion propagating in the fluctuating magnetized medium. Our analytical results reveal a leading double-logarithmic contribution ∼[ln(|eB|/m2)]2 to the mass, with an imaginary part representing a spectral broadening proportional to the magnetic noise autocorrelation Δ. While a uniform magnetic field already breaks Lorentz invariance, inducing the usual separation into two orthogonal subspaces (perpendicular and parallel with respect to the field), the presence of magnetic noise further breaks the remaining symmetry, thus leading to distinct spectral widths associated with fermion and antifermion, and their spin projection in the quasiparticle picture. Published by the American Physical Society 2024

Searches for violation of Lorentz invariance in top quark pair production using dilepton events in 13 TeV proton-proton collisions

A search for violation of Lorentz invariance in the production of top quark pairs (tt‾) is presented. The measured normalized differential tt‾ production cross section, as a function of the sidereal time, is examined for potential modulations induced by Lorentz-invariance breaking operators in an effective field theory extension of the standard model (SM). The cross section is measured from collision events collected by the CMS detector at a center-of-mass-energy of 13 TeV, corresponding to an integrated luminosity of 77.8 fb−1, and containing one electron and one muon. The results are found to be compatible with zero, in agreement with the SM, and are used to place upper limits at 68% confidence level on the magnitude of the Lorentz-violating couplings ranging from 1–8×10−3. This is the first precision test of the isotropy in special relativity with top quarks at the LHC, restricting further the bounds on such couplings by up to two orders of magnitude with respect to previous searches conducted at the Tevatron.

Stable Lorentz-breaking model for an antisymmetric two-tensor

In this work we investigate possible actions for antisymmetric two-tensor field models subject to constraints that force the field to acquire a nonzero vacuum expectation value, thereby spontaneously breaking Lorentz invariance. In order to assure stability, we require that the associate Hamiltonian be bounded from below. It is shown that this requirement rules out any quadratic action constructed only from the antisymmetric tensor field. We then explicitly construct a hybrid model consisting of the antisymmetric two-tensor field together with a vector field, subject to constraints forcing nonzero expectation values, that is stable in Minkowski space. Published by the American Physical Society 2024

Non-analyticity of the S-matrix with spontaneously broken Lorentz invariance

We study the S-matrix of Goldstones in the renormalizable theory of a U(1) complex scalar at finite charge, i.e. in a state that breaks Lorentz invariance. The theory is weakly coupled so that this S-matrix exists at all energies. Unlike the Lorentz invariant case, the resulting S-matrix is not analytic in the exchanged (complexified) four-momentum. The non-analyticities stem from the LSZ reduction formula, as a consequence of the energy-dependent mixing between the radial and Goldstone modes.

Nonrelativistic Dirac fermions on the torus

Two dimensional conformal field theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories.

Violation of the Landau-Yang theorem from infrared Lorentz symmetry breaking

Lorentz symmetry forbids decays of massive spin-1 particle like the Z0 into two massless photons, a result known as the Landau-Yang theorem. But it is known that infrared effects can break Lorentz invariance. Employing the construction of Mund et al. [1] which incorporated this Lorentz violation, we propose an interaction leading to the decay Z0→ 2γ and study the dependence of the decay on the parameter of this Lorentz violation.

Universal horizons and black hole spectroscopy in gravitational theories with broken Lorentz symmetry

The violation of Lorentz invariance (LI) in gravitational theories, which allows superluminal propagations, dramatically alters the causal structure of the spacetime and modifies the notion of black holes (BHs). Instead of metric horizons, now universal horizons (UHs) define the boundaries of BHs, within which a particle cannot escape to spatial infinities even with an infinitely large speed. Then, a natural question is how the quasi-normal modes (QNMs) of a BH are modified, if one considers the UH as its causal boundary. In this paper, we study in detail this problem in Einstein–Aether theory, a vector-tensor theory that violates LI but yet is self-consistent and satisfies all observations to date. Technically, this poses several challenges, including singularities of the perturbation equations across metric horizons and proper identifications of ingoing modes at UHs. After overcoming these difficulties, we show that the QNMs of the Schwarzschild BH, also a solution of Einstein–Aether theory, consist of two parts, the metric and aether parts. The QNMs of the metric perturbations are quite similar to those obtained in general relativity and are consistent with current observations of gravitational waves. But the ones from aether perturbations are different, and our numerical studies indicate that they are even not stable. The latter is consistent with our previous studies, which showed that the stealth Schwarzschild BH suffers a Laplacian instability along the angular direction. The method and techniques developed in this paper can be applied to the studies of QNMs in other theories of gravity with broken LI.

Modeling Clock Comparison Experiments to Test Special Relativity

The clock comparison experiments to test special relativity mainly include the Michelson–Morley experiment, Kennedy–Thorndike experiment, Ives–Stilwell experiment and the comparison experiment of atomic clocks in two locations. These experiments can be roughly classified as the comparison of two types of clocks: optical clocks and atomic clocks. Through the comparison of such clocks, Lorentz invariance breaking parameters in the RMS framework can be tested. However, in such experiments, the structural effects of optical clocks have been fully considered, yet the structural effects of atomic clocks have not been carefully studied. Based on this, this paper analyzes the structural effects of atomic clocks in detail and divides the experiments into six types: the comparison of two atomic clocks, two optical clocks, and atomic clocks and optical clocks placed in different and the same locations. Finally, correction parameters for the experimental measurements are given.

I-Love-Q relations in Hořava-Lifshitz gravity

Ho\v{r}ava-Lifshitz gravity is an alternative theory to general relativity which breaks Lorentz invariance in order to achieve an ultraviolet complete and power-counting renormalizable theory of gravity. In the low energy limit, Ho\v{r}ava-Lifshitz gravity coincides with a vector-tensor theory known as khronometric gravity. The deviation of khronometric gravity from general relativity can be parametrized by three coupling constants: $\alpha$, $\beta$, and $\lambda$. Solar system experiments and gravitational wave observations impose stringent bounds on $\alpha$ and $\beta$, while $\lambda$ is still relatively unconstrained ($\lambda\lesssim 0.01$). In this paper, we study whether one can constrain this remaining parameter with neutron star observations through the universal I-Love-Q relations between the moment of inertia (I), the tidal Love number (Love), and the quadrupole moment (Q), which are insensitive to details in the nuclear matter equation of state. To do so, we perturbatively construct slowly-rotating and weakly tidally-deformed neutron stars in khronometric gravity. We find that the I-Love-Q relations are independent of $\lambda$ in the limit $(\alpha,\beta) \to 0$. Although some components of the field equations depend on $\lambda$, we show through induction and a post-Minkowskian analysis that slowly-rotating neutron stars do not depend on $\lambda$ at all. Tidally deformed neutron stars, on the other hand, are modified in khronometric gravity (though the usual Love number is not modified, as mentioned earlier), and there are potentially new, non-GR Love numbers, though their observability is unclear. These findings indicate that it may be difficult to constrain $\lambda$ with rotating/tidally-deformed neutron stars.

Fractional Soft Limits of Scattering Amplitudes.

It is a common lore that the amplitude for a scattering process involving one soft Nambu-Goldstone boson should scale like an integer power of the soft momentum. We revisit this expectation by considering the 2→2 scattering of phonons in solids. We show that, depending on the helicities of the phonons involved in the scattering process, the scattering amplitude may in fact vanish like a fractional power of the soft momentum. This is a peculiarity of the 4-point amplitude, which can be traced back to (1)the (spontaneous or explicit) breaking of Lorentz invariance, and (2)the approximately collinear kinematics arising when one of the phonons becomes soft. Our results extend to the general class of nonrelativistic shift-invariant theories of a vector field.

κ -deformed complex scalar field: Conserved charges, symmetries, and their impact on physical observables

In this paper we revisit the model of $\kappa$-deformed complex scalar field. We find that this model possesses ten conserved Noether charges that form, under commutators, a representation of (undeformed) Poincar\'e algebra. It follows that the theory is relativistic and does not break Lorentz invariance. However the spacetime representation of boosts is not standard, and contains a non-local translation, different for positive and negative energy modes. It then follows that although the masses of particles and anti-particles are equal, the theory violates CPT symmetry in a subtle way. We explain why the Jost-Wightman-Greenberg theorem of equivalence of the Poincar\'e symmetry and CPT fails in our case. Finally, we discuss the phenomenological consequences of the theory and its possible observational signatures.

On Lorentz Invariant Complex Scalar Fields

We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, Ψ x ⟶ e i / ℏ f x Ψ x . We show that the spacetime-dependent phase f x is the most natural relativistic extension of the phase associated with the transformation rule for the nonrelativistic Schrödinger wave function when it is subjected to a Galilean transformation. We then generalize the previous analysis by postulating that Ψ x transforms according to the above rule under proper Lorentz transformations (boosts or spatial rotations). This is the most general transformation rule compatible with a Lorentz invariant physical theory whose observables are bilinear functions of the field Ψ x . We use the previous wave equations to describe several physical systems. In particular, we solve the bound state and scattering problems of two particles which interact both electromagnetically and gravitationally (static electromagnetic and gravitational fields). The former interaction is modeled via the minimal coupling prescription while the latter enters via an external potential. We also formulate logically consistent classical and quantum field theories associated with these Lorentz covariant wave equations. We show that it is possible to make those theories equivalent to the Klein-Gordon theory whenever we have self-interacting terms that do not break their Lorentz invariance or if we introduce electromagnetic interactions via the minimal coupling prescription. For interactions that break Lorentz invariance, we show that the present theories imply that particles and antiparticles behave differently at decaying processes, with the latter being more unstable. This suggests a possible connection between Lorentz invariance-breaking interactions and the matter-antimatter asymmetry problem.

Interplay of interactions and disorder at the charge density wave transition of two-dimensional Dirac semimetals

We consider the effects of weak quenched fermionic disorder on the quantum-phase transition between the Dirac semimetal and charge density wave (CDW) insulator in two spatial dimensions. The symmetry breaking transition is described by the Gross-Neveu-Yukawa (GNY) theory of Dirac fermions coupled to an Ising order parameter field. Treating the disorder using the replica method, we consider chemical potential, vector potential (gauge), and random mass disorders, which all arise from nonmagnetic charged impurities. We self-consistently account for the Landau damping of long-wavelength order-parameter fluctuations by using the nonperturbative RPA resummation of fermion loops and compute the renormalization-group (RG) flow to leading order in the disorder strength and $1/N$ ($N$ the number of Dirac fermion flavors). We find two fixed points, the clean GNY critical point, which is stable against weak disorder, and a dirty GNY multicritical point, at which the chemical potential disorder is finite and the other forms of disorder are irrelevant. We investigate the scaling of physical observables at this finite-disorder multicritical point which breaks Lorentz invariance and gives rise to distinct non-Fermi liquid behavior.

Thermodynamics and transport of holographic nodal line semimetals

We study various thermodynamic and transport properties of a holographic model of a nodal line semimetal (NLSM) at finite temperature, including the quantum phase transition to a topologically trivial phase, with Dirac semimetal-like conductivity. At zero temperature, composite fermion spectral functions obtained from holography are known to exhibit multiple Fermi surfaces. Similarly, for the holographic NLSM we observe multiple nodal lines instead of just one. We show, however, that as the temperature is raised these nodal lines broaden and disappear into the continuum one by one, so there is a finite range of temperatures for which there is only a single nodal line visible in the spectrum. We compute several transport coefficients in the holographic NLSM as a function of temperature, namely the charge and thermal conductivities, and the shear viscosities. By adding a new non-linear coupling to the model we are able to control the low frequency limit of the electrical conductivity in the direction orthogonal to the plane of the nodal line, allowing us to better match the conductivity of real NLSMs. The boundary quantum field theory is anisotropic and therefore has explicitly broken Lorentz invariance, which leads to a stress tensor that is not symmetric. This has important consequences for the energy and momentum transport: the thermal conductivity at vanishing charge density is not simply fixed by a Ward identity, and there are a much larger number of independent shear viscosities than in a Lorentz-invariant system.

Risking your NEC

Energy conditions, especially the null energy condition (NEC), are generically imposed on solutions to retain a physically sensible classical field theory and they also play an important role in the AdS/CFT duality. Using this duality, we study non-trivially deformed strongly coupled quantum field theories at large-Nc. The corresponding dual classical gravity constructions entail the use of radially non-monotonic D-brane distributions. The distributions are phenomenological in the sense that they do not correspond to the smearing of known probe D-brane embeddings. The gravity backgrounds are supersymmetric and hence perturbatively stable, and do not possess curvature singularities. There are no short-cuts through the bulk spacetime for signal propagation which assures that the field theory duals are causal. Nevertheless, some of our solutions violate the NEC in the gravity dual. In these cases the non-monotonicity of the D-brane distributions is reflected in the properties of the renormalization group flow: none of the c-functions proposed in the literature are monotonic. This further suggests that the non-monotonic behavior of the c-functions within previously known anisotropic backgrounds does not originate from the breaking of Lorentz invariance. We surmise that NEC violations induced by quantum corrections also need to be considered in holographic duals, but can be studied already at the classical level.

Analytic nonintegrability and S -matrix factorization

We formulate an equivalence between the 2-dim $\ensuremath{\sigma}$-model spectrum expanded on a nontrivial massive vacuum and a classical particle Hamiltonian with variable mass and potential. By considering methods of analytic Galoisian nonintegrability on the appropriate geodesics of the Hamiltonian system we algebraically constrain the particle masses at fixed time, such that integrability is allowed. Through our equivalence, this explicitly constrains the masses of the excited spectrum of the dual 2-dim theory in such a way to imply the $S$-matrix factorization and no particle production. In particular, the integrability of the classical particle system implies the factorization of the $S$-matrix in the dual quantum 2-dim theory. Our proposal provides also nontrivial evidence on the connection between integrability and $S$-matrix factorization for large class of theories with interactions that break Lorentz invariance.

Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field

In this work, I investigate the finite temperature Casimir effect due to a massive and charged scalar field that breaks Lorentz invariance in a CPT-even, aether-like way. I study the cases of Dirichlet and mixed (Dirichlet–Neumann) boundary conditions on a pair of parallel plates. I will not examine the case of Neumann boundary conditions since it produces the same results as Dirichlet boundary conditions. The main tool used in this investigation is the [Formula: see text]-function technique that allows me to obtain the Helmholtz free energy and Casimir pressure in the presence of a uniform magnetic field perpendicular to the plates. Three cases of Lorentz asymmetry are studied: timelike, spacelike and perpendicular to the magnetic field, spacelike and parallel to the magnetic field. Asymptotic cases of small plate distance, high temperature, strong magnetic field, and large mass will be considered for each of the three types of Lorentz asymmetry and each of the two types of boundary conditions examined. In all these cases, simple and very accurate analytic expressions of the thermal corrections to the Casimir energy and pressure are obtained and I discover that these corrections strongly depend on the direction of the unit vector that produces the breaking of the Lorentz symmetry.

Timelike geodesics in three-dimensional rotating Hořava AdS black hole

We study the motion of particles in the background of a three-dimensional rotating Ho\v{r}ava AdS black hole that corresponds to a Lorentz-violating version of the BTZ black hole and we analyze the effect of the breaking of Lorentz invariance in such motion by solving analytically the geodesic equations. Mainly, we find that Lorentz-violating version of the BTZ black hole posses a more rich geodesic structure, where the planetary and circular orbits are allowed, which does not occurs in the BTZ background.

Anomalous diffusion and Noether's second theorem.

Despite the fact that conserved currents have dimensions that are determined solely by dimensional analysis (and hence no anomalous dimensions), Nature abounds in examples of anomalous diffusion in which L∝t^{γ}, with γ≠1/2, and heat transport in which the thermal conductivity diverges as L^{α}. Aside from breaking of Lorentz invariance, the true common link in such problems is an anomalous dimension for the underlying conserved current, thereby violating the basic tenet of field theory. We show here that the phenomenological nonlocal equations of motion that are used to describe such anomalies all follow from Lorentz-violating gauge transformations arising from Noether's second theorem. The generalizations lead to a family of diffusion and heat transport equations that systematize how nonlocal gauge transformations generate more general forms of Fick's and Fourier's laws for diffusive and heat transport, respectively. In particular, the associated Goldstone modes of the form ω∝k^{α},α∈R are direct consequences of fractional equations of motion.

Collision of particles near a three-dimensional rotating Ho\u0159ava AdS black hole

We consider a three-dimensional rotating AdS black hole, which is a solution of Hořava gravity in the low-energy limit that corresponds to a Lorentz-violating version of the BTZ black hole, and we analyze the effect of the breaking of Lorentz invariance on the possibility that the black hole can act as a particle accelerator by analyzing the energy in the center-of-mass (CM) frame of two colliding particles in the vicinity of its horizons. We find that the critical angular momentum of particles increases when the Hořava parameter xi increases and when the aether parameter b increases. Also, the particles can collide on the inner horizon with arbitrarily high CM energy if one of the particles has a critical angular momentum, possible for the BSW process. Here it is essential that, while for the extremal BTZ black hole the particles with critical angular momentum only can exist on the degenerate horizon, for the Lorentz-violating version of the BTZ black hole the particle with critical angular momentum can exist in a region away from the degenerate horizon. It is worth mentioning that the results exposed in this manuscript can be applied for the covariant version of Hořava gravity, where the covariant definition of the center-of-mass energy is well defined.