Weyl gauging of topologically massive gravity

We construct a Weyl-invariant extension of topologically massive gravity, which remarkably turns out to include topologically massive electrodynamics, with a Proca mass term, conformally coupled to a scalar field. The action has no dimensionful parameters; therefore, the masses are generated via symmetry breaking either radiatively in flat backgrounds or spontaneously in constant curvature backgrounds. The broken phase of the theory, generically, has a single massive spin-2 and a massive spin-1 excitation. Chiral gravity in asymptotically anti-de Sitter spacetimes does not arise as a low energy theory, while chiral gravity in de Sitter spacetime is not ruled out.