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We examine the question of scale vs. conformal invariance for the linearizedEinstein-Hilbert action, which describes the IR fixed point of quantum gravity.In $D = 4$, although the action is not conformally invariant in the usualsense, we explicitly show that the theory is a conformal field theory at thelevel of correlation functions. In higher dimensions, we show that the theoryis scale but not conformally invariant, but can be embedded into a largernon-unitary conformal field theory, analogous to what has been found forMaxwell theory in $D>4$. We give evidence that similar statements are true forall free higher spin theories.

Scale vs. Conformal Invariance at the IR Fixed Point of Quantum Gravity