Noboru Nakanishi
The standard theory of elementary particle physics is modified in such a way that the Higgs boson becomes unobservable and Lorentz invariance is slightly violated at the level of the S-matrix. The basic technique of realizing these properties without violating the unitarity of the physical S-matrix is the use of the complex-ghost quantum field theory.
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We revisit Bjorken's model of spontaneous breakdown of Lorentz invariance. We show that the model possesses zero mass, spin zero (scalar) Nambu-Goldstone boson, in addition to the zero mass, spin one (vector) photon.
In a class of three-dimensional Abelian gauge theories with both light and heavy fermions, heavy chiral fermions can trigger dynamical generation of a magnetic field, leading to the spontaneous breaking of the Lorentz invaiance. Finite masses of light fermions tend to restore the Lorentz invariance.
In any theory with spontaneous symmetry breaking, it is important to account for the massless Nambu-Goldstone and massive Higgs modes. In this short review, the fate of these modes is examined for the case of a bumblebee model, in which Lorentz symmetry is spontaneously broken.
We consider a relativistic effective field theory of vector boson whose vacuum exhibits spontaneous breaking of Lorentz invariance. We argue that a simple model of this type, considered recently by Kraus and Tomboulis, is obstructed from having a consistent ultraviolet completion according to the diagnostic recently suggested by Adams, Arkani-Hamed, Dubovsky, Nicolis, and Rattazzi.
In a class of three-dimensional abelian gauge theory the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field. An originally topologically massive photon becomes gapless, i.e. p_0=0 at {\vec p}=0. Indeed, the photon is the Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance. Although symmetry generated by two Lorentz boost generators is broken, there seems to appear only one physical Nambu-Goldstone boson, namely a photon. We argue that the Ward identities in the Nambu-Goldstone theorem are saturated by the photon pole.
In a class of renormalizable three-dimensional abelian gauge theory the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field $B$. The true ground state resembles that of the quantum Hall effect. An originally topologically massive photon becomes gapless, fulfilling the role of the Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance. We give a simple explanation and a sufficient condition for the spontaneous breaking of the Lorentz invariance with the aid of the Nambu-Goldstone theorem. The decrease of the energy density by …
We study the vacuum solutions of a gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking (LSB), radial/temporal LSB and axial/temporal LSB. The purely radial LSB result corresponds to new black hole solutions. When possible, Parametrized Post-Newtonian (PPN) parameters are computed and observational boundaries used to constrain the Lorentz symmetry breaking scale.
We study the spontaneous Lorentz symmetry breaking in a field theoretical model in (2+1)-dimension, inspired by string theory. This model is a gauge theory of an anti-symmetric tensor field and a vector field (photon). The Nambu-Goldstone (NG) boson for the spontaneous Lorentz symmetry breaking is identified with the unphysical massless photon in the covariant quantization. We also discuss an analogue of the equivalence theorem between the amplitudes for emission or absorption of the physical massive anti-symmetric tensor field and those of the unphysical massless photon. The low-energy effect…
In Quantum Field Theory models with spontaneously broken gauge invariance, renormalizability limits to four the degree of the Higgs potential, whose minima determine the vacuum state at tree-level. In many models, this bound has the intriguing consequence of preventing the observability, at tree-level, of some phases that would be allowed by symmetry. We show that, generally, the phenomenon persists also if one-loop radiative corrections are taken into account. The tree-level unobservability of some phases is characteristic in two-Higgs-doublet extensions of the Standard Model with additional …
One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu-Goldstone bosons is obtained.
We re-examine three-dimensional gauge theory with a Chern-Simons term in which the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field. A non-vanishing magnetic field leads, through the Nambu-Goldstone theorem, to the decrease of zero-point energies of photons, which accounts for a major part of the mechanism. The asymmetric spectral flow plays an important role. The instability in pure Chern-Simons theory is also noted.
Spontaneous violation of Lorentz symmetry by the vacuum condensation of an antisymmetric $2$-tensor is considered. The coset construction for nonlinear realization of spacetime symmetries is employed to build the most general low-energy effective action for the Goldstone modes interacting with photons. We analyze the model within the context of the Standard-Model Extension and noncommutative QED. Experimental bounds for some parameters of the model are discussed, and we readdress the subtle issues of stability and causality in Lorentz non-invariant scenarios. Besides the two photon polarizatio…
We study a theory where the presence of an extra spin-two field coupled to gravity gives rise to a phase with spontaneously broken Lorentz symmetry. In this phase gravity is massive, and the Weak Equivalence Principle is respected. The newtonian potentials are in general modified, but we identify an non-perturbative symmetry that protects them. The gravitational waves sector has a rich phenomenology: sources emit a combination of massless and massive gravitons that propagate with distinct velocities and also oscillate. Since their velocities differ from the speed of light, the time of flight d…
We study nonlinear vacuum electrodynamics in a first-order formulation proposed by Plebański. By applying a Dirac constraint analysis, we derive an effective Hamiltonian, together with the equations of motion. We show that there exists a large class of potentials for which the effective Hamiltonian is bounded from below, while at the same time possessing stationary points in which the field strength acquires a nonzero vacuum expectation value. The associated spontaneous breaking of Lorentz symmetry can in principle be detected by coupling the model to a suitable external current, or to gravity…
We reconsider the possibility of violating the generalized second law of thermodynamics in theories with spontaneous Lorentz violation. It has been proposed that this may be accomplished in particular with a black hole immersed in a ghost condensate background, which may be taken to break Lorentz invariance without appreciably distorting the space-time geometry. In this paper we show that there in fact exist solutions explicitly describing flow of negative energy into these black holes, allowing for violation of the second law in a very simple way. This second law violation is independent of a…
Scalar QED is studied with higher order derivatives for the scalar field kinetic energy. A local potential is generated for the gauge field due to the covariant derivatives and the vacuum with non-vanishing expectation value for the scalar field and the vector potential is constructed in the leading order saddle point expansion. This vacuum breaks the global gauge and Lorentz symmetry spontaneously. The unitarity of time evolution is assured in the physical, positive norm subspace and the linearized equations of motion are calculated. Goldstone theorem always keeps the radiation field massless…
Many current models which "violate Lorentz symmetry" do so via a vector or tensor field which takes on a vacuum expectation value, thereby spontaneously breaking the underlying Lorentz symmetry of the Lagrangian. One common way to construct such a model is to posit a smooth potential for this field; the natural low-energy solution of such a model would then be excepted to have the tensor field near the minimum of its potential. It is shown in this work that some such models, while appearing well-posed at the level of the Lagrangian, have a Hamiltonian which is singular on the vacuum manifold a…
Gravitational wave solutions with spontaneous Lorentz symmetry breaking are studied. This breaking is triggered by a vector field, known as the bumblebee field. A brief analysis of the main consequences of this symmetry breaking on free-waves solutions and in the presence of matter sources are presented. For the free case, the modified wave equation for the gravitational perturbation field is solved, and we compare the polarization states with the usual solution. Considering a current that acts as a source of the radiation, we solve the equation of motion using the Green function method. Final…
We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-KR sector from the Higgs-KR sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z' boson of…
In this work, we study the spontaneous Lorentz symmetry breaking due to an antisymmetric 2-tensor field in Minkowski spacetime. For a smooth quadratic potential, the spectrum of the theory exhibits massless and massive excitations. We show that the equations of motion for the free field obey some constraints which lead to the massive mode be non-propagating at leading order. Besides, there exists a massless mode in the theory which can be identified with the usual Kalb-Ramond field, carrying only one on-shell degree of freedom. The same conclusion holds when one analyses the pole structure of …
We consider how Lorentz-violating interactions in the Faddeev-Popov ghost sector will affect scalar QED. The behavior depends sensitively on whether the gauge symmetry is spontaneously broken. If the symmetry is not broken, Lorentz violations in the ghost sector are unphysical, but if there is spontaneous breaking, radiative corrections will induce Lorentz-violating and gauge-dependent terms in other sectors of the theory.
A brief summary of some of the main consequences of spontaneous Lorentz violation in gravity is presented, including evasion of a no-go theorem, concomitant spontaneous diffeomorphism breaking, the appearance of massless Nambu-Goldstone modes and massive Higgs modes, and the possibility of a Higgs mechanism in gravity.
We extend a result by Ojima on spontaneous symmetry breaking of Lorentz boosts in thermal (KMS) states and show that it is in fact a special case in a more general class of examples of spontaneous symmetry breaking of Lorentz symmetry in relativistic many-body systems. Furthermore we analyse the nature of the corresponding Goldstone phenomenon and the type of Goldstone excitations (provided they have particle character).
In a wide class of three-dimensional Abelian gauge theories with a bare Chern-Simons term, the Lorentz invariance is spontaneously broken by dynamical generation of a non-vanishing magnetic field. A detailed computation of an energy density of the true vacuum is given. The originally massive photon becomes massless, fulfilling the role of a Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance.
We study the quantization of a simple model of antisymmetric tensor field with spontaneous Lorentz violation in curved spacetime. We evaluate the 1-loop corrections at first order of metric perturbation, using a general covariant effective action approach. We revisit the issue of quantum equivalence, and find that it holds for non-Lorentz-violating modes but breaks down for Lorentz violating modes.
Gauge-noninvariant vector field theories with superficially nonrenormalizable nonpolynomial interactions are studied. We show that nontrivial relevant and stable theories have spontaneous Lorentz violation, and we present a large class of asymptotically free theories. The Nambu-Goldstone modes of these theories can be identified with the photon, with potential experimental implications.
Spontaneous Lorentz violation is a viable mechanism to look for Planck scale physics. In this work, we study spontaneous Lorentz violation models, in flat spacetime, where a vector field produces such a violation and matter is modeled by a complex scalar field. We show that it is possible to construct a Hamilton density for which the evolution respects the dynamical constraints. However, we also find that the initial data, as required by standard field theory, does not determine the fields evolution in a unique way. In addition, we present some examples where the physical effects of such ambig…
Spontaneous breaking of Lorentz symmetry has been suggested as a possible mechanism that might occur in the context of a fundamental Planck-scale theory, such as string theory or a quantum theory of gravity. However, if Lorentz symmetry is spontaneously broken, two sets of questions immediately arise: what is the fate of the Nambu-Goldstone modes, and can a Higgs mechanism occur? A brief summary of some recent work looking at these questions is presented here.
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.
This paper has been withdrawn by the authors due to need of essential revision.
In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symm…
We present an explicit proof that a minimal model of rank-2 antisymmetric field with spontaneous Lorentz violation and a classically equivalent vector field model are also quantum equivalent, by calculating quantum effective actions of both theories. We comment on the issues encountered while checking quantum equivalence in curved spacetime.
Spontaneous Lorentz symmetry violation and topological defects for the Chern-Simons matter vector field
本文研究(1+2)D时空中Chern-Simons矢量场因自发洛伦兹对称性破缺产生的拓扑缺陷，将其分为涡旋和畴壁两类，并分析拓扑质量影响及稳定性，发现畴壁形成不稳定。
The metric-affine bumblebee model in the presence of fermionic matter minimally coupled to the connection is studied. We show that the model admits an Einstein frame representation in which the matter sector is described by a non-minimal Dirac action without any analogy in the literature. Such non-minimal terms involve unconventional couplings between the bumblebee and the fermion field. We then rewrite the quadratic fermion action in the Einstein frame in the basis of 16 Dirac matrices in order to identify the coefficients for Lorentz/CPT violation in all orders of the non-minimal coupling $ξ…
We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter `nu' which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue th…
We propose that local Lorentz invariance is spontaneously violated at high energies, due to a nonvanishing vacuum expectation value of a vector field ϕ^μ, as a possible explanation of the observation of ultra-high energy cosmic rays with an energy above the GZK cutoff. Certain consequences of spontaneous breaking of Lorentz invariance in cosmology are discussed.
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 investigate the compatibility of Lorentz-violating quantum field theories with the requirements of causality and stability. A general renormalizable model for free massive fermions indicates that these requirements are satisfied at low energies provided the couplings controlling the breaking are small. However, for high energies either microcausality or energy positivity or both are violated in some observer frame. We find evidence that this difficulty can be avoided if the model is interpreted as a sub-Planckian approximation originating from a nonlocal theory with spontaneous Lorentz viol…
It is shown that a spontaneously-broken gauge theory of the Lorentz group contains Ashtekar's chiral formulation of General Relativity accompanied by dust. From this perspective, gravity is described entirely by a connection $ω$ valued in the Lie algebra of the complexified Lorentz group and a Lorentz-charged scalar field $τ$. The model is "pre-geometric" in the sense that the spacetime metric may be constructed only in the symmetry-broken regime. We speculate on the extent to which this dust may account for dark matter and on the behaviour of the theory in regimes where the symmetry is not br…
We consider some aspects of spontaneous breaking of Lorentz Invariance in field theories, discussing the possibility that the certain tensor operators may condensate in the ground state in which case the tensor Goldstone particles would appear. We analyze their dynamics and discuss to which extent such a theory could imitate the gravity. We are also interested if the universality of coupling of such `gravitons' with other particles can be achieved in the infrared limit. Then we address the more complicated models when such tensor Goldstones coexist with the usual geometrical gravitons. At the …
We obtain an exact Kerr-like black hole solution by solving the corresponding gravitational field equations in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken once a vector field acquires a vacuum expectation value. Results are presented for the purely radial Lorentz symmetry breaking. In order to study the effects of this breaking, we consider the black hole shadow and find that the radial of the unstable spherical orbit on the equatorial plane $r_c$ decreases with the Lorentz breaking constant $\ell>0$, and increases with $\ell<0$. These shifts are similar to …
Frohlich, Morchio and Strocchi long ago proved that Lorentz invariance is spontaneously broken in QED because of infrared effects. We develop a simple model where consequences of this breakdown can be explicitly and easily calculated. For this purpose, the superselected U(1) charge group of QED is extended to a superselected "Sky" group containing direction-dependent gauge transformations at infinity. It is the analog of the Spi group of gravity. As Lorentz transformations do not commute with Sky, they are spontaneously broken. These abelian considerations and model are extended to non-Abelian…
In the Ashtekar-Barbero formulation of canonical general relativity based on an SU(2) connection, Lorentz covariance is a subtle issue which has been the focus of some debate. Here we present a Lorentz covariant formulation generalising the notion of a foliation of spacetime to a field of local observers which specify a time direction only locally. This field spontaneously breaks the local SO(3,1) symmetry down to a subgroup SO(3); we show that the apparent symmetry breaking to SO(3) is not in conflict with Lorentz covariance. We give a geometric picture of our construction as Cartan geometrod…
The issue of spontaneous breaking of Lorentz and CPT invariance is studied in the open bosonic string using a truncation scheme to saturate the string-field action at successively higher levels. We find strong evidence for the existence of extrema of the action with nonzero expectation values for certain fields. The Lorentz- and CPT-preserving solution previously suggested in the literature is confirmed through level 12 in the action. A family of Lorentz-breaking, CPT-preserving solutions of the equations of motion is found to persist and converge through level 18 in the action. Two sequences …
The fate of the Nambu-Goldstone modes arising from spontaneous Lorentz violation is investigated. Using the vierbein formalism, it is shown that up to 10 Lorentz and diffeomorphism Nambu-Goldstone modes can appear and that they are contained within the 10 modes of the vierbein associated with gauge degrees of freedom in a Lorentz-invariant theory. A general treatment of spontaneous local Lorentz and diffeomorphism violation is given for various spacetimes, and the fate of the Nambu-Goldstone modes is shown to depend on both the spacetime geometry and the dynamics of the tensor field triggering…
Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type $A_μA^μ=M^{2}$ ($M$ is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possib…
Constitutive Origin of Hamiltonian Degeneracy in Nonlinear Electrodynamics with Spontaneous Lorentz Symmetry Breaking
研究非线性电动力学中自发洛伦兹对称破缺下，哈密顿退化结构的构成起源，揭示磁真空有效哈密顿量与磁响应的关系及退化机制。
It is by now clear that infrared sector of QED has an intriguingly complex structure. Based on earlier pioneering works on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the $U(1)$ charge group of QED to the "Sky" group incorporating the known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality. There it was shown that the "Sky" group is generated by the algebra of angle dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous bre…
We reconsider an alternative theory of the QED with the photon as a massless vector Nambu-Goldstone boson and show that the underlying spontaneous Lorentz violation caused by the vector field vacuum expectation value, while being superficial in gauge invariant theory, becomes physically significant in the QED with a tiny gauge non-invariance. This leads, through special dispersion relations appearing for charged fermions, to a new class of phenomena which could be of distinctive observational interest in particle physics and astrophysics. They include a significant change in the GZK cutoff for…
Considering quantum gravity within the framework of effective field theory, we investigated the consequences of spontaneous Lorentz violation for the gravitational potential. In particular, we focus our attention on the bumblebee models, in which the graviton couples to a vector $B_μ$ that assumes a nonzero vacuum expectation value. The leading order corrections for the nonrelativistic potential are obtained from calculation of the scattering matrix of two scalar particles interacting gravitationally. These corrections imply anisotropic properties associated with the bumblebee background and a…
In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking (SSB) seems to occur, so that only one extended direction remains, as first observed by Bialas, Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where …
We consider a class of field theories with a four-vector field $A_μ(x)$ in addition to other fields supplied with a global charge symmetry - theories which have partial gauge symmetry in the sense of only imposing it on those terms in the Lagrangian density which have derivatives as factors in them. We suppose that spontaneous Lorentz invariance breaking occurs in such a theory due to the four-vector field taking a non-zero vacuum expectation value. Under some very mild assumptions, we show that this Lorentz violation is not observable and the whole theory is practically gauge invariant. A ver…
In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between such modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended un…
After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding non-linear gauge A_μA^μ=n^{2}M^{2}. Our result is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the…
Hamiltonian Constraints on Spontaneous Lorentz Symmetry Breaking in the Bumblebee Model
本文通过分析哈密顿结构和约束，指出传统通过拉格朗日势最小值确定自发洛伦兹破缺的方法不正确，提出应通过哈密顿密度确定真真空，并证明二次势无法一致产生真空期望值，而三次势是更可行的替代方案。
Spontaneous breaking of local Lorentz symmetry occurs when a local vector or tensor field acquires a nonzero vacuum expectation value. The effects of such breaking are examined in the context of gravity theory. These include an associated spontaneous breaking of diffeomorphism symmetry and generation of massless Nambu-Goldstone modes. The possibility of a Higgs mechanism is examined as well, and it is found that the conventional Higgs mechanism (giving rise to massive gauge fields) does not occur in a Riemann spacetime. However, in a Riemann-Cartan spacetime a Higgs mechanism involving the spi…
We generalize the coset construction of Callan, Coleman, Wess and Zumino to theories in which the Lorentz group is spontaneously broken down to one of its subgroups. This allows us to write down the most general low-energy effective Lagrangian in which Lorentz invariance is non-linearly realized, and to explore the consequences of broken Lorentz symmetry without having to make any assumptions about the mechanism that triggers the breaking. We carry out the construction both in flat space, in which the Lorentz group is a global spacetime symmetry, and in a generally covariant theory, in which t…
We argue that non-Abelian gauge fields can be treated as the pseudo-Goldstone vector bosons caused by spontaneous Lorentz invariance violation (SLIV). To this end, the SLIV which evolves in a general Yang-Mills type theory with the nonlinear vector field constraint $Tr(% \boldsymbol{A}_{μ}\boldsymbol{A}^μ)=\pm M^{2}$ ($M$ is a proposed SLIV scale) imposed is considered in detail. With an internal symmetry group $G$ having $D$ generators not only the pure Lorentz symmetry SO(1,3), but the larger accidental symmetry $SO(D,3D)$ of the SLIV constraint in itself appears to be spontaneously broken a…
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…
Lorentz-violating operators involving Standard Model fields are tightly constrained by experimental data. However, bounds are more model-independent for Lorentz violation appearing in purely gravitational couplings. The spontaneous breaking of Lorentz invariance by the vacuum expectation value of a vector field selects a universal rest frame. This affects the propagation of the graviton, leading to a modification of Newton's law of gravity. We compute the size of the long-range preferred-frame effect in terms of the coefficients of the two-derivative operators in the low-energy effective theor…
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