Regular Article - Theoretical Physics
Note on Weyl versus conformal invariance in field theory
Department of Physics, Nanchang University, Nanchang, 330031, China
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Accepted: 11 December 2017
Published online: 19 December 2017
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.
© The Author(s), 2017