Note on Weyl versus conformal invariance in field theory

作者:Wu, Feng*
来源:European Physical Journal C, 2017, 77(12): 886.
DOI:10.1140/epjc/s10052-017-5463-8

摘要

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.