Note on Weyl versus Conformal Invariance in Field Theory

Abstract

It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that generically unitarity alone is not sufficient for a conformal field theory to be Weyl invariant. Furthermore, we show explicitly that when a unitary conformal field theory couples to gravity in a Weyl invariant way, each primary scalar operator that is either relevant or marginal in the unitary conformal field theory corresponds to a Weyl-covariant operator in the curved background.

10 pages, v3: version to appear in EPJC

References in corpus (1)

• Restricted Weyl invariance in four-dimensional curved spacetime

Cited by in corpus (5)

• Weyl Connections and their Role in Holography
• On the Conformal Symmetry of Exceptional Scalar Theories
• Renormalizing Spacetime
• Conformal invariance versus Weyl invariance
• Compactifications of String/M-Theory and the Swampland: A Study of the AdS${}_{\text{4}}$ Mass Spectrum of Eleven-Dimensional Supergravity on the Squashed Seven-Sphere