On Emergent Gauge and Gravity Theories

We present some general approach to emergent gauge theories and consider in significant detail the emergent tensor field gravity case. In essence, an arbitrary local theory of a symmetric two-tensor field $H_{\mu \nu}$ in Minkowski spacetime is considered, in which the equations of motion are required to be compatible with a nonlinear $\sigma$ model type length-fixing constraint $H_{\mu \nu}^{2}=\pm M^{2}$ 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. The underlying diffeomophism invariance emerges as a necessary condition for the tensor field $H_{\mu \nu}$ 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.Comment: 10 pages, Invited talk given at the International Workshop "Low dimensional physics and gauge principles" (21-29 September 2011, Yerevan-Tbilisi), to appear in the Conference Proceedings (World Scientific, 2012

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 among 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 photon may only contain true Goldstone modes, graviton appears at least partially composed from pseudo-Goldstone modes rather than from 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 that is considered in some detail. How this emergent electrogravity theory could be observationally differed from conventional QED and GR theories is also briefly discussed.Comment: 22 pages, to appear in Eur. Phys. Journ. C. arXiv admin note: text overlap with arXiv:1008.370

Massless and Massive Vector Goldstone Bosons in Nonlinear Quantum Electrodynamics

The spontaneous Lorentz invariance violation (SLIV) developing in QED type theories with the nonlinear four-vector field constraint $A_{\mu}^{2}=M^{2}$ (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.Comment: To appear in Proceedings of the XIVth International Seminar ``Quarks-2006'' (18-24 May 2006, St-Petersburg, Russia