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

TL;DR

This paper investigates the relationship between scale and conformal invariance in the IR fixed point of quantum gravity, revealing dimension-dependent invariance properties and embedding into larger conformal theories.

Contribution

It demonstrates that the linearized Einstein-Hilbert action is conformally invariant in 4D at the correlation function level and shows scale but not conformal invariance in higher dimensions, with embeddings into non-unitary CFTs.

Findings

In 4D, the theory is a conformal field theory at the correlation level.

In higher dimensions, the theory is scale invariant but not conformally invariant.

The theory can be embedded into a larger non-unitary conformal field theory.

Abstract

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 non-unitary 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.