A quantum field model for Dirac-like tachyons respecting a frame-dependent interpretation rule, and thus inherently breaking Lorentz invariance, is defined. It is shown how the usual paradoxa ascribed to tachyons, instability and acausality, are resolved in this model, and it is argued elsewhere that Lorentz symmetry breaking is necessary to permit perturbative renormalizability and causality. Elimination of negative-normed states results in only left-handed particles and right-handed antiparticles, suitable for describing the neutrino. In this context the neutron beta decay spectrum is calculated near the end point for large, but not ultrarelativistic preferred frame speed, assuming a vector weak interaction vertex.
Current experiments do not exclude the possibility that one or more neutrinos are very slightly superluminal or that they have a very small tachyonic mass. Important bounds on the size of a hypothetical tachyonic neutrino mass term are set by lepton pair Cerenkov radiation (LPCR), i.e., by the decay channel nu -> e^+ e^- nu which proceeds via a virtual Z0 boson. Here, we use a Lorentz-invariant dispersion relation which leads to very tight constraints on the tachyonic mass of neutrinos; we also calculate decay and energy loss rates. A possible cutoff seen in the IceCube neutrino spectrum for E…
The emission of a charged light lepton pair by a superluminal neutrino has been identified as a major factor in the energy loss of highly energetic neutrinos. The observation of PeV neutrinos by IceCube implies their stability against lepton pair Cerenkov radiation. Under the assumption of a Lorentz-violating dispersion relation for highly energetic superluminal neutrinos, one may thus constrain the Lorentz-violating parameters. A kinematically different situation arises when one assumes a Lorentz-covariant, space-like dispersion relation for hypothetical tachyonic neutrinos, as an alternative…
We discuss the recent scenario of tachyonic preheating at the end of inflation as a consequence of a tachyonic mass term in the scalar field responsible for spontaneous symmetry breaking. We use 3D lattice simulations to expore this very non-perturbative and non-linear phenomenon, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential.
Spontaneous symmetry breaking usually occurs due to the tachyonic (spinodal) instability of a scalar field near the top of its effective potential at $ϕ= 0$. Naively, one might expect the field $ϕ$ to fall from the top of the effective potential and then experience a long stage of oscillations with amplitude O(v) near the minimum of the effective potential at $ϕ= v$ until it gives its energy to particles produced during these oscillations. However, it was recently found that the tachyonic instability rapidly converts most of the potential energy V(0) into the energy of colliding classical wave…
We reconsider the old problem of the dynamics of spontaneous symmetry breaking using 3d lattice simulations, and develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that symmetry breaking typically completes within a single oscillation of the field distribution as it rolls towards the minimum of its effective potential. As an application of this theory we consider preheating in the hybrid inflation scenario, including SUSY-motivated F-term and D-term inflationary models. We show that preheating in hybr…
A consistent quantization scheme for imaginary-mass field is proposed. It is related to an appropriate choice of the synchronization procedure (definition of time), which guarantee an absolute causality in agreement with Lorentz covariance. In that formulation a possible existence of field excitations (tachyons) distinguish an inertial frame (tachyon privileged frame of reference) {\em via} spontaneous breaking of the so called synchronization group. In this scheme relativity principle is broken but Lorentz symmetry is exactly preserved in agreement with local properties of the observed world.
Recent time-of-flight measurements on muon neutrinos in the OPERA neutrino oscillation experiment have found anomalously short times compared to the light travel-times, corresponding to a superluminal velocity, $v-1=2.37\pm0.32\times 10^{-5}$ in units where $c=1$. We show that cosmological bounds rule out an explanation involving a Lorentz invariant tachyonic neutrino. At the OPERA energy scale, nucleosynthesis constraints imply $v-1<0.86\times 10^{-12}$ and the Cosmic Microwave Background observations imply $v-1<7.1\times 10^{-23}$. The CMB limit on the velocity of a tachyon with an energy of…
The decoupling of scalar particles in split supersymmetry makes the spectrum of squarks irrelevant for low energy processes. Nevertheless, the structure of the vacuum is sensitive to the spectrum of squarks, even when the supersymmetry breaking scale is large. In this note, we show that in certain regions of the parameter space, squarks could develop radiatively tachyonic masses, thus breaking electric charge and color. We discuss the constraints that follow from the requirement of charge and color conservation, and we comment on the implications for model building.
The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packets in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, w…
We apply a new approach based on three relativistic groups (bradyon, tachyon and instanton) forming the `Lorentz groupoid' which allows, in particular, to consider tachyons without introducing imaginary masses and negative energies (related, as known, to violation of causality and unitarity). This leads to effectively scalar conglomerate composed of tachyonic neutrino and antineutrino spinor wave functions as a viable model for stationary dark matter. We also briefly discuss a relevant early non-stationary high-energy stage of the universe evolution.
Superconformal anomalies provide an elegant and economical way to understand the soft breaking parameters in SUSY models; however, implementing them leads to the several undesirable features including: tachyonic sleptons and electroweak symmetry breaking problems in both the MSSM and the NMSSM. Since these two theories also have the additonal problem of massless neutrinos, we have reconsidered the AMSB problems in a class of models that extends the NMSSM to explain small neutrino masses via the seesaw mechanism. In a recent paper, we showed that for a class of minimal left-right extensions, a …
We consider in detail the calculation of the decay rate of high-energy superluminal neutrinos against (charged) lepton pair Cerenkov radiation (LPCR), and neutrino pair Cerenkov radiation (NPCR), i.e., against the decay channels nu -> nu e+ e- and nu -> nu nubar nu. Under the hypothesis of a tachyonic nature of neutrinos, these decay channels put constraints on the lifetime of high-energy neutrinos for terrestrial experiments as well as on cosmic scales. For the oncoming neutrino, we use the Lorentz-covariant tachyonic relation E_nu = (p^2 - m_nu^2)^(1/2), where m_nu is the tachyonic mass para…
Motivated by a recent and several earlier measurement results of the neutrino velocity, we attempt to resolve the apparent discrepancies between them from the viewpoint of mass-energy relation in special relativity. It is argued that a complicated tachyonic neutrino model or a mass-dependent Lorentz violation theory can do this job.
A tiny Lorentz symmetry breaking can be mediated in Electrodynamics by means of the Chern-Simons (CS) interaction polarized along a constant CS vector. Its presence makes the vacuum optically active that has been recently estimated from astrophysical data. We examine two possibilities for the CS vector to be time-like or space-like, under the assumption that it originates from v.e.v. of some pseudoscalar matter. It is shown that: a) a time-like CS vector makes the vacuum unstable under pairs creation of tachyonic photon modes with the finite vacuum decay rate, i.e. it is unlikely realized at m…
We revive the historically first dark matter model based on neutrinos, but with an additional assumption that neutrinos might exist in tachyonic almost sterile states. To this end, we propose a group-theoretical algorithm for the description of tachyons. The key point is that we employ a distinct tachyon Lorentz group with new (superluminal) parametrization which does not lead to violation of causality and unitarity. Our dark matter model represents effectively scalar tachyonic neutrino-antineutrino conglomerate. Distributed all over the universe, such fluid behaves as stable isothermal/stiff …
We suggest that the electroweak Higgs particles can be identified with extra-dimensional components of the gauge fields, which after compactification on a certain topologically non-trivial background become tachyonic and condense. If the tachyonic mass is a tree level effect, the natural scale of the gauge symmetry breaking is set by the inverse radius of the internal space, which, in case of the electroweak symmetry, must be around $\sim 1/$TeV. We discuss the possibility of a vanishing tree level mass for the Higgs. In such a scenario the tachyonic mass can be induced by quantum loops and ca…
With the help of the tachyonic trapping mechanism one can potentially solve a number of problems affecting quintessential inflation models. In this mechanism we introduce a trapping field with a spontaneous symmetry breaking potential. When the quintessential inflaton passes the critical point, a sudden burst of particle production is able to reheat the Universe and trap the inflaton away from theminimum of its potential. However, self-interactions of the trapping field suppress particle production and reduce the efficiency of this process. We develop a method to compute the magnitude of the s…
We explore two distinct resolutions to the tachyonic slepton puzzle in the Anomaly Mediated Supersymmetry Breaking scenario. Both are based on extending the MSSM by an anomaly free U(1) symmetry, and in both cases exact RG invariance is preserved.
By carefully studying the (1,0)+(0,1) representation space for massive particles we point to the existence of certain inherent tachyonic dispersion relations: E^2= p^2-m^2. We put forward an interpretation that exploits these ``negative mass squared'' solutions; rotational invariance is spontaneously broken. Relevance of these results to the vortices in the cosmos is pointed out. NOTE: Just as "negative energy solutions'' of Dirac equation are re-interpreted as antiparticles, similarly the possibility exists for re-interpreting the tachyonic dispersion relations of all (j,0)+(0,j) representati…
Motivated by the severity of the bounds on Lorentz violation in the presence of ordinary gravity, we study frameworks in which Lorentz violation does not affect the spacetime geometry. We show that there are at least two inequivalent classes of spontaneous Lorentz breaking that even in the presence of gravity result in Minkowski space. The first one generically corresponds to the condensation of tensor fields with tachyonic mass which in turn is related to ghost-condensation. In the second class, realized by the DGP model or theories of massive gravitons, spontaneous Lorentz breaking is induce…
The new results by OPERA collaboration claim the discovery of superluminal neutrinos. Superluminal particles have to break Lorentzian symmetry or causality principle. The method discussed gives us the possibility to reintroduce Lorentzian symmetry without breaking of causality.
The toy fermion model coupled with Lagrange multiplier constraint field is proposed. The possibility of superluminal neutrino propagation as result of dynamical Lorentz symmetry breaking is studied.
We study the generation of aether-like Lorentz-breaking actions in three, four and five dimensions via an appropriate Lorentz-breaking coupling of electromagnetic and spinor fields. Special attention is given to the four-dimensional case where we discuss the issue of ambiguities.
Gravitational theories with Lorentz violation must account for a number of possible features in order to be consistent theoretically and phenomenologically. A brief summary of these features is given here. They include evasion of a no-go theorem, connections between spontaneous Lorentz breaking and diffeomorphism breaking, the appearance of massless Nambu-Goldstone modes and massive Higgs modes, and the possibility of a Higgs mechanism in gravity.
Generally speaking, the existence of a superluminal neutrino can be attributed either to re-entrant Lorentz violation at ultralow energy from intrinsic Lorentz violation at ultrahigh energy or to spontaneous breaking of fundamental Lorentz invariance (possibly by the formation of a fermionic condensate). Re-entrant Lorentz violation in the neutrino sector has been discussed elsewhere. Here, the focus is on mechanisms of spontaneous symmetry breaking.
Combining anomaly with Z' mediation allows us to solve the tachyonic slepton problem of the former and avoid fine tuning in the latter. We describe how the two mechanisms can be combined, and some of the phenomenology of such a joint scenario.
We investigate nonlinear extensions of the holographic soft wall model proposed by Karch, Katz, Son and Stephanov \cite{Karch:2006pv} with a positive quadratic dilaton. We consider a Higgs potential for the tachyonic field that brings a more natural realisation of chiral symmetry breaking in the infrared regime. Utilising the AdS/CFT dictionary and holographic renormalisation we find the chiral condensate as a function of the quark mass. The nonlinearity of the Higgs potential leads to a nonlinear relation between the chiral condensate and the quark mass. Solving the effective Schrödinger equa…
In the context of N=4 supergravity in four dimensions, we present an exact classical solution that leads to spacetime-dependent electromagnetic couplings and discuss the ensuing Lorentz-violating effects. We comment briefly on experimental bounds.
The breakdown of spacetime symmetries has recently been identified as a promising candidate signal for underlying physics, possibly arising through quantum-gravitational effects. This talk gives an overview over various aspects of CPT- and Lorentz-violation research. Particular emphasis is given to the interplay between CPT, Lorentz, and translation symmetry, mechanisms for CPT and Lorentz breaking, and the construction of a low-energy quantum-field description of such effect. This quantum field framework, called the SME, is employed to determine possible phenomenological consequences of CPT a…
The Lorentz nature of confinement in a heavy-light quarkonium is investigated. It is demonstrated that an effective scalar interaction is generated selfconsistently as a result of chiral symmetry breaking, and this effective scalar interaction is responsible for the QCD string formation between the quark and the antiquark.
We study the quantum stability of Type IIB orbifold and orientifold string models in various dimensions, including Melvin backgrounds, where supersymmetry (SUSY) is broken {\it à la} Scherk-Schwarz (SS) by twisting periodicity conditions along a circle of radius R. In particular, we compute the R-dependence of the one-loop induced vacuum energy density $ρ(R)$, or cosmological constant. For SS twists different from Z2 we always find, for both orbifolds and orientifolds, a monotonic $ρ(R)<0$, eventually driving the system to a tachyonic instability. For Z2 twists, orientifold models can have a d…
One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of such effects into a low-energy effective field theory is presented. An extension of the standard model that includes Lorentz- and CPT-breaking terms is developed. The restriction of the standard model extension to the QED sector is then discussed.
Low-energy remnant fundamental symmetry violations may be present in nature at levels attainable in upcoming experiments. These effects may arise through spontaneous symmetry breaking in a more complete Lorentz covariant theory underlying the standard model. In this work the issue of parameterizing such violations in a consistent and complete manner is addressed. The approach is to use the mechanism of spontaneous symmetry breaking to generate all possible terms consistent with gauge invariance and power-counting renormalizability to construct an extension of the standard model that includes L…
If one modifies the Dirac equation in momentum space to $[γ^μp_μ-m-Δm(θ(p_{0})-θ(-p_{0})) θ(p_μ^{2})]ψ(p)=0$, the symmetry of positive and negative energy eigenvalues is lifted by $m\pm Δm$ for a small $Δm$. The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations $θ(\pm p_{0})θ(p_μ^{2})$ with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but non-local at a distance scale of the Planck length. The application of this Lo…
We analyze the unitarity of a modified QED with higher-order terms that violate Lorentz symmetry. We make an explicit calculation to verify unitarity at the one-loop level. As expected we find negative norm states that could in principle lead to a violation of unitarity. However, we show that these states become massive in Euclidean space and do not contribute to the discontinuity.
Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a non-vanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.
Based on models of confinement of quarks, we analyse a relativistic scalar particle subject to a scalar potential proportional to the inverse of the radial distance and under the effects of the violation of the Lorentz symmetry. We show that the effects of the Lorentz symmetry breaking can induced a harmonic-type potential. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background of the violation of the Lorentz symmetry on the relativistic energy levels.
We calculate higher-order quantum contributions in different Lorentz-violating parameters to the gauge sector of the extended QED. As a result of this one-loop calculation, some terms which do not produce first-order corrections, contribute with nontrivial gauge-invariant second-order quantum inductions.
Anomaly mediated supersymmetry breaking implemented in the minimal supersymmetric standard model (MSSM) is known to suffer from the tachyonic slepton problem leading to breakdown of electric charge conservation. We show however that when MSSM is extended to explain small neutrino masses by gauging the B-L symmetry, the slepton masses can be positive due to the Z' mediation contributions. We obtain various soft supersymmetry breaking mass spectra, which are different from those obtained in the conventional anomaly mediation scenario. Then there would be a distinct signature of this scenario at …
We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear electrodynamics. The model is stable in the small Lorentz invariance violation approximation. The speed of light is independent of the frequency and one of the propagating modes is highly anisotropic. The bound (Delta c)/c < 10^{-32} is obtained for such anisotropy measured in perpendicular directions.
Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a…
The lagrangian-based Standard-Model Extension framework offers a broad description of possible gravitational effects from local Lorentz violation. In this talk, I review the status of the theoretical and phenomenological work in this area. The extension of previous results in linearized gravity to the nonlinear regime is discussed.
In this paper we derive acoustic black hole metrics in the (3+1) and (2+1)-dimensional Abelian Higgs model with Lorentz symmetry breaking. In this set up the sound waves lose the Lorentz boost invariance and suffer a 'birefringence' effect. We have found acoustic black holes and respective Hawking temperatures depending on the Lorentz violating parameter. Furthermore, we obtain an acoustic Kerr-like black hole metric with the Lorentz violating term affecting its rate of loss of mass. We also have shown that for suitable values of the Lorentz violating parameter a wider spectrum of particle wav…
We complete the set of spin-projector operators for fields up to rank-3 by providing all operators connecting sectors with same spin and parity. In this way we can broaden the search for unitary and non-tachyonic particle propagation in quadratic lagrangian with inter-field mixing. We use the properties of projector algebra to reanalyze known theories and shed light towards new healthy ones. We do so with full control over the gauge constraints by working the form of the saturated propagator in an appropriate frame of reference.
We study the effect of spontaneous breaking of Lorentz invariance on black hole thermodynamics. We consider a scenario where Lorentz symmetry breaking manifests itself by the difference of maximal velocities attainable by particles of different species in a preferred reference frame. The Lorentz breaking sector is represented by the ghost condensate. We find that the notions of black hole entropy and temperature loose their universal meaning. In particular, the standard derivation of the Hawking radiation yields that a black hole does emit thermal radiation in any given particle species, but w…
We consider an extended QED with the addition of a dimension-five Lorentz-breaking coupling between spinor and gauge fields, involving a pseudo-tensor $κ^{μνλρ}$. The specific form of the Lorentz violating coupling considered by us have been suggested in other works, and some of its consequences at the classical level were already studied. Here, we investigate the consequences of this specific form of Lorentz violation at the quantum level, evaluating the one loop corrections to the gauge field two-point function, both at zero and at finite temperature. We relate the terms that are generated b…
A number of different approaches to quantum gravity are at least partly phenomenologically characterized by their treatment of Lorentz symmetry, in particular whether the symmetry is exact or modified/broken at the smallest scales. For example, string theory generally preserves Lorentz symmetry while analog gravity and Lifshitz models break it at microscopic scales. In models with broken Lorentz symmetry there are a vast number of constraints on departures from Lorentz invariance that can be established with low energy experiments by employing the techniques of effective field theory in both t…
Many candidate fundamental theories contain scalar fields that can acquire spacetime-varying expectation values in a cosmological context. Such scalars typically obey Lorentz-violating effective dispersion relations. We illustrate this fact within a simple supergravity model that also exhibits the observed late-time cosmological acceleration and implies varying electromagnetic couplings.
In this work, we investigate the dynamical breakdown of Lorentz symmetry in 4 dimensions by the condensation of a fermionic field described by a Dirac Lagrangian with a four-fermion interaction. Using the Keldysh formalism we show that the Lorentz symmetry breaking modifies the Dyson-Schwinger equations of the fermionic propagator. We analyze the nonperturbative solutions for the Dyson-Schwinger equations using the combination of the rainbow and quenched approximations and show that, in equilibrium, the Lorentz symmetry breakdown can occur in the strong coupling regime and new features arise f…
Recent studies suggest that the process of symmetry breaking after inflation typically occurs very fast, within a single oscillation of the symmetry-breaking field, due to the spinodal growth of its long-wave modes, otherwise known as `tachyonic preheating'. We show how this sudden transition from the false to the true vacuum can induce a significant production of particles, bosons and fermions, coupled to the symmetry-breaking field. We find that this new mechanism of particle production in the early Universe may have interesting consequences for the origin of supermassive dark matter and the…
We describe how a stable effective theory in which particles of the same fermion number attract may spontaneously break Lorentz invariance by giving non-zero fermion number density to the vacuum (and therefore dynamically generating a chemical potential term). This mecanism yields a finite vacuum expectation value $<\barψγ^μψ>$ which we consider in the context of proposed models that require such a breaking of Lorentz invariance in order to yield composite degrees of freedom that act approximately like gauge bosons. We also make general remarks about how the background source provided by $<\ba…
We extend the Minimum Supersymmetry Standard Model by a non-anomalous family (NAF) U(1)'_{NAF} gauge symmetry. All gauge anomalies are cancelled with no additional exotics other than the three right-handed neutrinos. The FI D-terms associated with the U(1)'_{NAF} symmetry lead to additional positive contributions to slepton squared masses. In a RG invariant way, this thus solves the tachyonic slepton mass problem in Anomaly Mediated Supersymmetry Breaking. In addition, the U (1)'_{NAF} symmetry naturally gives rise to the fermion mass hierarchy and mixing angles, and determines the mass spectr…
Spontaneous breaking of Lorentz invariance may take place in string theories, possibly endowing the photon with a mass. This leads to the breaking of the conformal symmetry of the electromagnetic action allowing for the generation within inflationary scenarios of magnetic fields over $Mpc$ scales. We show that the generated fields are consistent with amplification by the galactic dynamo processes and can be as large as to explain the observed galactic magnetic fields through the collapse of protogalactic clouds.
Phantom fields with negative kinetic energy are often plagued by the vacuum quantum instability in the ultraviolet region. We present a Lorentz-violating dark energy model free from this problem and show that the crossing of the cosmological constant boundary w=-1 to the phantom equation of state is realized before reaching a de Sitter attractor. Another interesting feature is a peculiar time-dependence of the effective Newton's constant; the magnitude of this effect is naturally small but may be close to experimental limits. We also derive momentum scales of instabilities at which tachyons or…
A popular framework for exploring Lorentz violation is the Standard Model Extension. This extension contains a large number of parameters that can be bounded in various experiments. Most studies, however, focus on the fermion or photon sector. Here, we consider Lorentz violation in the weak vector boson sector. The strongest bounds come from measurements of the asymmetry in Moller scattering. We study the bounds that can be obtained from future measurements of the parity violating asymmetry in deep inelastic electron-proton scattering at the EIC, the LHeC and the FCC-eh. For the FCC-eh, the bo…
