what happened to the Nambu-Goldstone bosons?
For a discrete symmetry like CPT, Goldstone’s theorem doesn’t apply. For global Lorentz symmetry, it implies that spontaneous breaking must be accompanied by massless bosons. These modes might be identified with the photon. If gravity is included then Lorentz symmetry becomes local. In gauge theories the Nambu-Goldstone bosons could be absorbed to generate masses for the gauge bosons according to the Higgs mechanism, but we have shown the analogue of this effect doesn’t occur for gravity. Instead, in some gravitational theories the massless bosons might again be identified with the photon, while in others (with propagating spin connection) the massless bosons can be absorbed to generate mass terms in analogy with the usual Higgs mechanism.
