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

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.

arXiv comment11 pages. v2 typos fixed, version appearing in PRD

References in corpus (12)

• Implications of Conformal Invariance in Field Theories for General Dimensions
• Introduction to Effective Field Theory
• What Maxwell Theory in D<>4 teaches us about scale and conformal invariance
• On Scale and Conformal Invariance in Four Dimensions
• Conformal correlators of mixed-symmetry tensors
• Conformally Covariant Differential Operators: Properties and Applications
• New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order
• On four-point interactions in massless higher spin theory in flat space
• Notes on conformal invariance of gauge fields
• Scale-invariant breaking of conformal symmetry
• Irreversibility and higher-spin conformal field theory
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering

Cited by in corpus (8)

• Gravity as a gapless phase and biform symmetries
• An improved Noether's theorem for spacetime symmetries
• Scale and Conformal Invariance on (A)dS
• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• On the possibility of a novel (A)dS/CFT relationship emerging in Asymptotic Safety
• Entanglement entropy of a Rarita-Schwinger field in a sphere
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• Scale without Conformal Invariance in bottom-up Holography