Note on Weyl versus conformal invariance in field theory
Note on Weyl versus conformal invariance in field theory
复制标题
关于场论中外尔与共形不变性的注释
DOI：
10.1140/epjc/s10052-017-5463-8
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发表时间：
2017
影响因子：
4.4
通讯作者：
Wu Feng
中科院分区：
文献类型：
--
作者：
Wu Feng
最近有人提出平坦时空中的共形不变性意味着酉理论在一般弯曲背景下的Weyl不变性，并指出标量算子的Weyl变化中可能存在的异常。我们论证了一个共形场论仅具有一般的唯一性是不足以成为Weyl不变的。进一步，我们明确地证明了当幺正共形场论与重力以weyl不变方式耦合时，在幺正共形场论中相关或边缘的每一个主标量算子对应于弯曲背景中的一个weyl协变算子。
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.