Scale versus conformal invariance at the IR fixed point of quantum gravity

We examine the question of scale vs conformal invariance for the linearized Einstein-Hilbert action, which describes the IR fixed point of quantum gravity. In D = 4, although the action is not conformally invariant in the usual sense, we explicitly show that the theory is a conformal field theory at the level of correlation functions. In higher dimensions, we show that the theory is scale but not conformally invariant, but can be embedded into a larger nonunitary conformal field theory, analogous to what has been found for Maxwell theory in D > 4. We give evidence that similar statements are true for all free higher-spin theories.