Is the Graviton a Goldstone Boson?

Abstract

A theory is outlined in which Lorentz invariance is spontaneously violated, giving rise to a constant vector field X*. The two quantities which are most simply related to A* are the gravitational constant g and the decay rate of K<P -» 2w, assuming that the latter will eventually show an energy dependence. Using a method suggested by Bjorken for electrodynamics, we conclude that the model may support a graviton, and determine the order of magnitude of Q. A simple argument relates the K 2° decay to g; the agreement with experiment is good.

Photon and photino as Nambu–Goldstone zero modes in an emergent SUSY QED

“…This old idea [3][4][5], supported by a close analogy with the dynamical origin of massless particle excitations for spontaneously broken internal symmetries, has gained new impetus in recent years. On the other hand, besides its generic implication for the possible origin of physical gauge fields [6][7][8][9][10][11][12] in a conventional quantum field theory (QFT) framework, there are many different contexts in the literature where Lorentz violation may stem itself from string theory [13,14], quantum gravity [15] or any unspecified dynamics at an ultraviolet scale perhaps related to the Planck scale [16][17][18][19][20][21][22].…”

“…This model contains, among other terms, the inappropriately large (while false; see below) Lorentz-violating fermion bilinear −eMψ(n μ γ μ )ψ. This term appears when the effective Higgs mode expansion in Goldstone modes a μ [as is given in the parametrization (4)] is applied to the fermion current interaction term −eψγ μ A μ ψ in the QED Lagrangian (7). However, due to local invariance this bilinear term can be gauged away by making an appropriate redefinition of the fermion field ψ → e −ieω(x) ψ with a gauge function ω(x) linear in coordinates, ω(x) = (n μ x μ )M. Meanwhile, the dimension-five Lagrangian L dim 5 (6) is substantially changed under this redefinition, which significantly modifies the fermion bilinear terms…”

Spontaneous Breaking of Lorentz-Invariance and Gravitons as Goldstone Particles

“…The terms with higher then two powers of derivatives in (5) can lead to higher order in "curvature" terms in L, and near to the "Planck" scale where ∂ µ ∼ Λ all these terms can be of same order as L 2 Here again as for L 2 we come two type of terms. Terms that we construct by using only the covariant t µν for contraction of indices and other terms -in which η µν and t µν are also used.…”

“…This idea was further extended to nonabelian case and also [2]- [3] to tensor condensates and corresponding goldstones were interpreted as graviton-like objects. The possibility to represent some or all gauge fields and gravitons as the Goldstone particles connected with fluctuations of vector and tensor condensates can seem quite promising.…”

On the spontaneous breaking of lorentz invariance

“…Indeed, a background cosmological vector field has been considered as a way to introduce our velocity with respect to a preferred frame of reference into the physical description [11]. It has also been proposed, based on the behaviour of the renormalization group β−function of non-abelian gauge theories, that Lorentz invariance could be actually a low-energy symmetry [12].…”