Spontaneous Lorentz Invariance Violation Research Articles

On the lightlike Lorentz violation

We consider the lightlike spontaneous Lorentz invariance violation (SLIV) appearing through the zero “length-fixing” constraint put on a gauge vector field, AμAμ=0, and discuss its physical consequences in the framework of a conventional QED and beyond. Again, as in the timelike and spacelike SLIV cases, AμAμ=±MA2 (MA is a scale of SLIV), while this constraint leads to an emergence of the Nambu-Goldstone modes collected in physical photon, the SLIV itself is still left unobservable unless gauge invariance in the theory is broken. At the same time, a crucial difference with the two former cases is that the asymmetrical vacuum corresponding to the lightlike Lorentz violation appears infinitely degenerated with all other vacua including the symmetrical one. We show that this degeneracy can be lifted out by introducing an extra gauge vector field being sterile with respect to an ordinary matter, though having some potential couplings with the basic Aμ field. A slight mixing of them makes the underlying gauge invariance to be partially broken due to which physical Lorentz invariance occurs broken as well. This may cause a variety of the Lorentz violating processes some of which are briefly discussed.

Lorentzian Goldstone modes shared among photons and gravitons

It has long been known that photons and gravitons may appear as vector and tensor Goldstone modes caused by spontaneous Lorentz invariance violation (SLIV). Usually this approach is considered for photons and gravitons separately. We develop the emergent electrogravity theory consisting of the ordinary QED and the tensor-field gravity model which mimics the linearized general relativity in Minkowski spacetime. In this theory, Lorentz symmetry appears incorporated into higher global symmetries of the length-fixing constraints put on the vector and tensor fields involved, A_{mu }^{2}=pm M_{A}^{2} and H_{mu nu }^{2}=pm M_{H}^{2} (M_{A} and M_{H} are the proposed symmetry breaking scales). We show that such a SLIV pattern being related to breaking of global symmetries underlying these constraints induces the massless Goldstone and pseudo-Goldstone modes shared by photon and graviton. While for a vector field case the symmetry of the constraint coincides with Lorentz symmetry SO(1, 3) of the electrogravity Lagrangian, the tensor-field constraint itself possesses much higher global symmetry SO(7, 3), whose spontaneous violation provides a sufficient number of zero modes collected in a graviton. Accordingly, while the photon may only contain true Goldstone modes, the graviton appears at least partially to be composed of pseudo-Goldstone modes rather than of pure Goldstone ones. When expressed in terms of these modes, the theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. However, all SLIV effects turn out to be strictly cancelled in the lowest order processes considered in some detail. How this emergent electrogravity theory could be observationally different from conventional QED and GR theories is also briefly discussed.

Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime

Recently, Kostelecky [V.A. Kostelecky, Phys. Lett. B 701, 137 (2011)] proposed that the spontaneous Lorentz invariance violation (sLIV) is related to Finsler geometry. Finsler spacetime is intrinsically anisotropic and naturally induces Lorentz invariance violation (LIV). In this paper, the electromagnetic field is investigated in locally Minkowski spacetime. The Lagrangian is presented explicitly for the electromagnetic field. It is compatible with the one in the standard model extension (SME). We show the Lorentz-violating Maxwell equations as well as the electromagnetic wave equation. The formal plane wave solution is obtained for the electromagnetic wave. The speed of light may depend on the direction of light and the lightcone may be enlarged or narrowed. The LIV effects could be viewed as influence from an anisotropic media on the electromagnetic wave. In addition, birefringence of light will not emerge at the leading order in this model. A constraint on the spacetime anisotropy is obtained from observations on gamma-ray bursts (GRBs).

Standard model with partial gauge invariance

We argue that an exact gauge invariance may disable some generic features of the Standard Model which could otherwise manifest themselves at high energies. One of them might be related to the spontaneous Lorentz invariance violation (SLIV) which could provide an alternative dynamical approach to QED and Yang-Mills theories with photon and non-Abelian gauge fields appearing as massless Nambu-Goldstone bosons. To see some key features of the new physics expected we propose partial rather than exact gauge invariance in an extended SM framework. This principle applied, in some minimal form, to the weak hypercharge gauge field B_{mu} and its interactions leads to SLIV with B field components appearing as the massless Nambu-Goldstone modes, and provides a number of distinctive Lorentz beaking effects. Being naturally suppressed at low energies they may become detectable in high energy physics and astrophysics. Some of the most interesting SLIV processes are considered in significant detail.

Spontaneously generated tensor field gravity

An arbitrary local theory of a symmetric two-tensor field H μ ν in Minkowski spacetime is considered, in which the equations of motion are required to be compatible with a nonlinear length-fixing constraint H μ ν 2 = ± M 2 leading to spontaneous Lorentz invariance violation, SLIV ( M is the proposed scale for SLIV). Allowing the parameters in the Lagrangian to be adjusted so as to be consistent with this constraint, the theory turns out to correspond to linearized general relativity in the weak field approximation, while some of the massless tensor Goldstone modes appearing through SLIV are naturally collected in the physical graviton. In essence the underlying diffeomorphism invariance emerges as a necessary condition for the tensor field H μ ν not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in the theory is chosen by SLIV. The emergent theory appears essentially nonlinear, when expressed in terms of the pure Goldstone tensor modes and contains a plethora of new Lorentz and CPT violating couplings. However, these couplings do not lead to physical Lorentz violation once this tensor field gravity is properly extended to conventional general relativity.

Graviton as a Goldstone boson: Nonlinear sigma model for tensor field gravity

Spontaneous Lorentz invariance violation (SLIV) realized through a nonlinear tensor field constraint Hμν2=±M2 (M is the proposed scale for Lorentz violation) is considered in tensor field gravity theory, which mimics linearized general relativity in Minkowski space–time. We show that such a SLIV pattern, due to which the true vacuum in the theory is chosen, induces massless tensor Goldstone modes some of which can naturally be associated with the physical graviton. When expressed in terms of the pure Goldstone modes, this theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings. Nonetheless, all SLIV effects turn out to be strictly canceled in all the lowest order processes considered, provided that the tensor field gravity theory is properly extended to general relativity (GR). So, as we generally argue, the measurable effects of SLIV, induced by elementary vector or tensor fields, are related to the accompanying gauge symmetry breaking rather than to spontaneous Lorentz violation. The latter appears by itself to be physically unobservable, only resulting in a non-covariant gauge choice in an otherwise gauge invariant and Lorentz invariant theory. However, while Goldstonic vector and tensor field theories with exact local invariance are physically indistinguishable from conventional gauge theories, there might appear some principal distinctions if this local symmetry were slightly broken at very small distances in a way that could eventually allow one to differentiate between them observationally.

Lorentz violation in warped extra dimensions

Higher dimensional theories which address some of the problematic issues of the Standard Model(SM) naturally involve some form of $D=4+n$-dimensional Lorentz invariance violation (LIV). In such models the fundamental physics which leads to, e.g., field localization, orbifolding, the existence of brane terms and the compactification process all can introduce LIV in the higher dimensional theory while still preserving 4-d Lorentz invariance. In this paper, attempting to capture some of this physics, we extend our previous analysis of LIV in 5-d UED-type models to those with 5-d warped extra dimensions. To be specific, we employ the 5-d analog of the SM Extension of Kostelecky et. al. ~which incorporates a complete set of operators arising from spontaneous LIV. We show that while the response of the bulk scalar, fermion and gauge fields to the addition of LIV operators in warped models is qualitatively similar to what happens in the flat 5-d UED case, the gravity sector of these models reacts very differently than in flat space. Specifically, we show that LIV in this warped case leads to a non-zero bulk mass for the 5-d graviton and so the would-be zero mode, which we identify as the usual 4-d graviton, must necessarily become massive. The origin of this mass term is the simultaneous existence of the constant non-zero $AdS_5$ curvature and the loss of general co-ordinate invariance via LIV in the 5-d theory. Thus warped 5-d models with LIV in the gravity sector are not phenomenologically viable.

Spontaneous Lorentz violation: Non-Abelian gauge fields as pseudo-Goldstone vector bosons

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(AμAμ)=±M2 (M is a proposed SLIV scale) imposed is considered in detail. Specifically, we show that in a theory 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 as well. As a result, although the pure Lorentz violation on its own still generates only one genuine Goldstone vector boson, the accompanying pseudo-Goldstone vector bosons related to the SO(D,3D) breaking also come into play properly completing the whole gauge multiplet of the internal symmetry group G taken. Remarkably, they appear to be strictly massless as well, being protected by the starting non-Abelian gauge invariance of the Yang–Mills theory involved. When expressed in terms of the pure Goldstone vector modes, this theory look essentially nonlinear and contains a plethora of Lorentz and CPT violating couplings. However, they do not lead to physical SLIV effects which turn out to be strictly cancelled in all the lowest order processes considered.

Nonlinear massive QED and physical Lorentz invariance

Abstract The spontaneous Lorentz invariance violation (SLIV) developing in QED type theories with the nonlinear four-vector field constraint A μ 2 = M 2 (where M is a proposed scale of the Lorentz violation) is considered in the case when the internal U ( 1 ) charge symmetry is also spontaneously broken. We show that such a SLIV pattern induces the genuine vector Goldstone boson which appears massless when the U ( 1 ) symmetry is exact and becomes massive in its broken phase. However, for both of phases an apparent Lorentz violation is completely canceled out in all the observable processes so that the physical Lorentz invariance in theory is ultimately restored.