https://doi.org/10.1140/epjc/s10052-017-5463-8
Regular Article - Theoretical Physics
Note on Weyl versus conformal invariance in field theory
Department of Physics, Nanchang University, Nanchang, 330031, China
* e-mail: fengwu@ncu.edu.cn
Received:
23
October
2017
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
