Spontaneous symmetry breakdown of scale symmetries

We discuss spontaneous symmetry breakdown (SSB) of both global and local scale symmetries in scalar-tensor gravity with two scalar fields, one of which couples nonminimally to scalar curvature while the other is a normal scalar field.In case of a global scale symmetry, by moving from the Jordan frame to the Einstein frame, a normal scalar field becomes massive while the dilaton remains massless after the SSB.In case of a local scale symmetry, we take a gauge fixing condition for the local scale invariance, aR + bφ 2 = k, which was found in our previous study of a Weyl's quadratic gravity.Together with locally scale invariant potential terms in a classical action, this gauge condition generates a Higgs potential whose vacuum expectation value (VEV) produces the Einstein-Hilbert action with an R 2 term in the lowest level of approximation.One interesting aspect in this model is that a massless Nambu-Goldstone boson associated with a scale invariance is absorbed into the metric tensor field and consequently an R 2 term is induced in the action.