ar X iv : 0 90 1 . 07 96 v 3 [ he p - th ] 1 4 M ay 2 00 9 Vector - Field Domain Walls

We argue that spontaneous Lorentz violation may generally lead to metastable domain walls related to the simultaneous violation of some accompanying discrete symmetries. Remarkably, such domain wall solutions exist for space-like Lorentz violation and do not exist for the time-like violation. Because a preferred space direction is spontaneously induced, these domain walls have no planar symmetry and produce a peculiar static gravitational field at small distances, while their longdistance gravity appears the same as for regular scalar-field walls. Some possible applications of vector-field domain walls are briefly discussed. 1 Gauge fields as vector Nambu-Goldstone bosons Relativistic invariance and local gauge symmetries are cornerstones of our current understanding of elementary particles and their interactions. Elementary particles as quanta of their corresponding fields are classified through irreducible representations of the Poincaré group, while the local gauge symmetries prescribe their dynamics. This theoretical picture is most successfully realized within the celebrated Standard Model of quarks and leptons and their fundamental strong, weak and electromagnetic interactions. Nevertheless, it is conceivable that local gauge symmetries and the associated masslessness of gauge bosons might have a completely different origin, being in essence dynamical rather than due to a fundamental principle. This point of view is partially motivated by the peculiarities of local gauge symmetries themselves, which, unlike global symmetries, represent redundancies of the description of a theory rather than being “true” symmetries. In addition, the dynamical origin of massless particle excitations is very well understood in terms of spontaneously broken global symmetries. Based on these observations, the origin of massless gauge fields as the vector Nambu-Goldstone bosons appearing due to spontaneous Lorentz invariance violation (SLIV) [1] has gained new impetus [2]-[7] in recent years.1 While the first models realizing the SLIV conjecture were based on the four fermion interaction (where the photon was expected to appear as a fermion-antifermion composite state [1]), the simplest model for SLIV is in fact given by a conventional QED type Lagrangian extended by an arbitrary vector field potential energy. For the minimal polynomial containing only the vector field bilinear and quadrilinear terms one comes to the Lagrangian L = − 4 FabF ab − λ 4 (