Breaking Of Lorentz Invariance Research Articles

Coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model

We discuss the coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model to study supersymmetry breaking for these fermions. We find that the coupled model has two distinct solutions. The first solution represents a local minimum of the superpotential which spontaneously breaks supersymmetry in perfect analogy to the O'Raifeartaigh model. The second solution is more intriguing as it corresponds to a global minimum of the superpotential. In this case, the coupling to the fermionic sector restores supersymmetry. However, this is achieved at the cost of breaking Lorentz invariance. Finally, the mass matrices for the multiplets of the coupled model are presented. It turns out that it contains two bosonic triplets and one fermionic doublet which are mass multiplets. In addition, it contains a massless fermionic doublet as well as one fermionic triplet which is not a mass multiplet but rather an interaction multiplet that contains component fields of different mass dimension. The results also imply that the presented model for fermionic fields with mass dimension one is an interesting candidate for supersymmetric dark matter (DM).

Classical and quantum ghosts

The aim of these notes is to provide a self-contained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence is associated with a classical instability whenever the ghost field interacts with standard fields. We then show that the instability is more severe at quantum level, and that perturbative ghosts can exist only in low energy effective theories. However, if we do not consider very ad hoc choices, compatibility with observational constraints implies that low energy effective ghosts can exist only at the price of giving up Lorentz invariance or locality above the cut-off, in which case the cut-off has to be much lower that the energy scales we currently probe in particle colliders. We also comment on the possible role of extra degrees of freedom which break Lorentz invariance spontaneously.

Parametrized post-Newtonian expansion and FRW scalar perturbations inn-DBI gravity

n-DBI gravity explicitly breaks Lorentz invariance by the introduction of a unit time-like vector field, thereby giving rise to an extra (scalar) degree of freedom. We look for observational consequences of this mode in two setups. Firstly, we compute the parametrized post-Newtonian (PPN) expansion of the metric to first post-Newtonian order. Surprisingly, we find that the PPN parameters are exactly the same as in General Relativity (GR), and no preferred-frame effects are produced. In particular this means that n-DBI gravity is consistent with all GR solar system experimental tests. We discuss the origin of such degeneracy between n-DBI gravity and GR, and suggest it may also hold in higher post-Newtonian order. Secondly, we study gravitational scalar perturbations of a Friedmann-Robertson-Walker space-time with a cosmological constant $\Lambda \geq 0$. In the case of de Sitter space, we show that the scalar mode grows as the universe expands and, in contrast with a canonical scalar field coupled to GR, it does not freeze on super horizon scales.

Covariant renormalizable modified and massive gravity theories on (non)commutative tangent Lorentz bundles

The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Hořava–Lifshitz (HL); Einstein–Finsler gravity extensions etc.) possess an important decoupling property with respect to nonholonomic frames with 2 (or 3) + 2 + 2 + ⋯ spacetime decompositions. This allows us to construct exact solutions with generic off-diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un-)broken symmetry parameters. Such nonholonomic configurations/models have a nice ultraviolet behavior and seem to be ghost-free and (super-)renormalizable in a sense of covariant and/or massive modifications of HL gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into fibers of noncommutative tangent Lorentz bundles for corresponding "partner" anisotropically induced theories. We show how the constructions can be extended to include conjectured covariant renormalizable models with massive graviton fields and effective Einstein fields with (non)commutative variables.

Constraints on renormalization group flows from holographic entanglement entropy

We examine the RG flow of a candidate $c$ function, extracted from the holographic entanglement entropy of a strip-shaped region, for theories with broken Lorentz invariance. We clarify the conditions on the geometry that lead to a breakdown of monotonic RG flows as is expected for generic Lorentz-violating field theories. Nevertheless we identify a set of simple criteria on the UV behavior of the geometry which guarantee a monotonic $c$ function. Our analysis can thus be used as a guiding principle for the construction of monotonic RG trajectories and can also prove useful for excluding possible IR behaviors of the theory.

Multi-time Schrödinger equations cannot contain interaction potentials

Multi-time wave functions are wave functions that have a time variable for every particle, such as \documentclass[12pt]{minimal}\begin{document}$\phi (t_1,{\bm x}_1,\ldots ,t_N,{\bm x}_N)$\end{document}ϕ(t1,x1,...,tN,xN). They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, “Multi-time wave functions for quantum field theory,” Ann. Physics (to be published)]. We also prove the following result: When a cut-off length δ > 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schrödinger equations with interaction potentials of range δ are consistent; however, in the desired limit δ → 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.

Matter-enhanced transition probabilities in quantum field theory

The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths.

CPT and Lorentz Invariance: Their Relation and Violation

The CPT theorem in quantum field theory, its validity, breaking and consequences are reviewed. One can show that for CPT theorem to hold, Lorentz invariance is not always needed. Also one can have CPT violation, while there is Lorentz invariance. Field theoretical examples for both cases are given and mass differences between particle-antiparticle are discussed as well. Unambiguous tests of CPT violation, unrelated to the breaking of Lorentz invariance, are suggested.

Cosmological constraints on Lorentz violating dark energy

The role of Lorentz invariance as a fundamental symmetry of nature hasbeen lately reconsidered in different approaches to quantum gravity.It is thus natural to study whether other puzzles of physics may besolved within these proposals. This may be the case for thecosmological constant problem. Indeed, it has been shown that breakingLorentz invariance provides Lagrangians that can drive the currentacceleration of the universe without experiencing large correctionsfrom ultraviolet physics. In this work, we focus on the simplestmodel of this type, called ΘCDM, and study its cosmologicalimplications in detail. At the background level, this model cannot bedistinguished from ΛCDM. The differences appear at the levelof perturbations. We show that in ΘCDM, the spectrum of CMBanisotropies and matter fluctuations may be affected by a rescaling ofthe gravitational constant in the Poisson equation, by the presence ofextra contributions to the anisotropic stress, and finally by theexistence of extra clustering degrees of freedom. To explore thesemodifications accurately, we modify the Boltzmann code class.We then use the parameter inference code Monte Python toconfront ΘCDM with data from WMAP-7, SPT and WiggleZ. We obtainstrong bounds on the parameters accounting for deviations fromΛCDM. In particular, we find that the discrepancy between thegravitational constants appearing in the Poisson and Friedmannequations is constrained at the level of 1.8%.

Search for CPT and Lorentz invariance violation with neutral kaons at KLOE

The neutral kaon system offers a unique possibility to perform fundamental tests of fundamental symmetry such CP and CPT invariance. In this contribution the KLOE search for CPT symmetry and Lorentz Invariance breaking in the Standard Model Extension framework is reported. Preliminary results are:

Supersymmetric multicritical point in a model of lattice fermions

We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder, which has microscopic supersymmetry. It has been conjectured that in the continuum, the model is described by the superconformal minimal model with central charge $c=3/2$. Thus far, it has not been possible to confirm this conjecture due to strong finite-size corrections in numerical data. We trace the origin of these corrections to the presence of unusual marginal operators that break Lorentz invariance but preserve part of the supersymmetry. By relying mostly on entanglement entropy calculations with the density-matrix renormalization group, we are able to reduce finite-size effects significantly. This allows us to unambiguously determine the continuum theory of the model. We also study perturbations of the model and establish that the supersymmetric model is a multicritical point. Our work underlines the power of entanglement entropy as a probe of the phases of quantum many-body systems.

A discussion on Lorentz preserving scalar fields in Lorentz violating theory

Lorentz symmetry can be preserved in effective higher derivative scalar field theories containing a constant vector that breaks Lorentz invariance of flat spacetime, through the choice of special field configurations. These fields do satisfy the equations of motion, yielding cubic dispersion relations analogous to those derived earlier. Moreover, the Lie algebra of the Lorentz group can be realised on these fields.

Scalar graviton inn-DBI gravity

n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac's theory of constrained systems. Firstly, studying scalar perturbations around Minkowski space-time, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formalism, using ADM variables. It is useful to introduce an auxiliary scalar field, which allows recasting n-DBI gravity in an Einstein-Hilbert form but in a Jordan frame. Identifying the constraints and their classes we confirm the existence of an extra degree of freedom in the full theory, besides the two usual tensorial modes of the graviton. We then argue that, unlike the case of (the original proposal for) Horava-Lifschitz gravity, there is no evidence that the extra degree of freedom originates pathologies, such as vanishing lapse, instabilities and strong self-coupling at low energy scales.

Quantum Superpositions of the Speed of Light

While it has often been proposed that, fundamentally, Lorentz-invariance is not respected in a quantum theory of gravity, it has been difficult to reconcile deviations from Lorentz-invariance with quantum field theory. The most commonly used mechanisms either break Lorentz-invariance explicitly or deform it at high energies. However, the former option is very tightly constrained by experiment already, the latter generically leads to problems with locality. We show here that there exists a third way to integrate deviations from Lorentz-invariance into quantum field theory that circumvents the problems of the other approaches. The way this is achieved is an extension of the standard model in which photons can have different speeds without singling out a preferred restframe, but only as long as they are in a quantum superposition. Once a measurement has been made, observables are subject to the laws of special relativity, and the process of measurement introduces a preferred frame. The speed of light can take on different values, both superluminal and subluminal (with respect to the usual value of the speed of light), without the need for Lorentz-invariance violating operators and without tachyons. We briefly discuss the relation to deformations of special relativity and phenomenological consequences.

Spontaneously broken Lorentz invariance from the dynamics of a heavy sterile neutrino

A relativistic theory for neutrino superluminality is presented (in principle, the same mechanism applies also to other fermions). The theory involves the standard-model particles and one additional heavy sterile neutrino with an energy-scale close to or above the electroweak one, all particles propagating in the usual 3+1 spacetime dimensions. Lorentz violation results from spontaneous symmetry breaking in the sterile-neutrino sector. The theory tries, as far as possible, to be consistent with the existing experimental data from neutrino physics and to keep the number of assumptions minimal. There are clear experimental predictions which can be tested.

Axions and cosmic rays

We investigate the propagation of a charged particle in a spatially constant but time dependent pseudoscalar background. Physically this pseudoscalar background could be provided by a relic axion density. The background leads to an explicit breaking of Lorentz invariance; as a consequence processes such as $p\to p \gamma$ or $e\to e \gamma$ are possible within some kinematical constraints. The phenomenon is described by the QED lagrangian extended with a Chern-Simons term that contains a 4-vector which characterizes the breaking of Lorentz invariance induced by the time-dependent background. While the radiation induced (similar to the Cherenkov effect) is too small to influence the propagation of cosmic rays in a significant way, the hypothetical detection of the photons radiated by high energy cosmic rays via this mechanism would provide an indirect way of verifying the cosmological relevance of axions. We discuss on the order of magnitude of the effect.

Hořava gravity versus thermodynamics: The black hole case

Under broad assumptions breaking of Lorentz invariance in gravitational theories leads to tension with unitarity because it allows for processes that apparently violate the second law of thermodynamics. The crucial ingredient of this argument is the existence of black hole solutions with the interior shielded from infinity by a causal horizon. We study how the paradox can be resolved in the healthy extension of Horava gravity. To this aim we analyze classical solutions describing large black holes in this theory with the emphasis on their causal structure. The notion of causality is subtle in this theory due to the presence of instantaneous interactions. Despite this fact, we find that within exact spherical symmetry a black hole solution contains a space-time region causally disconnected from infinity by a surface of finite area -- the `universal horizon'. We then consider small perturbations of arbitrary angular dependence in the black hole background. We argue that aspherical perturbations destabilize the universal horizon and, at non-linear level, turn it into a finite-area singularity. The causal structure of the region outside the singularity is trivial. If the higher-derivative terms in the equations of motion smear the singularity while preserving the trivial causal structure of the solutions, the thermodynamics paradox would be obviated. As a byproduct of our analysis we prove that the black holes do not have any non-standard long-range hair. We also comment on the relation with Einstein-aether theory, where the solutions with universal horizon appear to be stable.

Consequences of neutrino Lorentz violation for leptonic meson decays

If the observation by OPERA of apparently superluminal neutrinos is correct, the Lagrangian for second-generation leptons must break Lorentz invariance. We calculate the effects of an energy-independent change in the neutrino speed on another observable, the charged pion decay rate. The rate decreases by a factor $[1\ensuremath{-}\frac{3}{1\ensuremath{-}{m}_{\ensuremath{\mu}}^{2}/{m}_{\ensuremath{\pi}}^{2}}(⟨{v}_{\ensuremath{\nu}}⟩\ensuremath{-}1)]$, where $⟨{v}_{\ensuremath{\nu}}⟩$ is the (directionally averaged) neutrino speed in the pion's rest frame. This provides a completely independent experimental observable that is sensitive to the same forms of Lorentz violation as a neutrino time-of-flight measurement.

Quantum 3D superstrings

The classical Green-Schwarz superstring action, with $\mathcal{N}=1$ or $\mathcal{N}=2$ spacetime supersymmetry, exists for spacetime dimensions $D=3$, 4, 6, 10, but quantization in the light-cone gauge breaks Lorentz invariance unless either $D=10$, which leads to critical superstring theory, or $D=3$. We give details of results presented previously for the bosonic and $\mathcal{N}=1$ closed 3D (super)strings and extend them to the $\mathcal{N}=2$ 3D superstring. In all cases, the spectrum is parity-invariant and contains anyons of irrational spin.

Electrodynamics of Abrikosov vortices: the field theoretical formulation

Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principle. We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the AC Josephson relation. On a deeper level, we explore the electrodynamics of two-form sources in the absence of electric monopoles, in which the electromagnetic field strength itself acquires the characteristics of a gauge field. This novel framework leaves room for unexpected surprises.