论文标题
在本地和集成的应力调整换向器上
On Local and Integrated Stress-Tensor Commutators
论文作者
论文摘要
我们讨论了洛伦兹CFT中本地运营商的换向者的一些一般方面，这些方面可以从欧几里得运营商产品扩展（OPE）的合适分析延续中获得。换向器仅作为分布才有意义，并且必须注意从OPE中提取正确的分布。我们在两个和四维的CFT中提供明确的计算，主要集中在应力调整器组件的换向器上。我们重新评估了几个熟悉的结果，例如自由田间理论的规范换向关系，庞加莱代数的局部形式以及二维CFT的Virasoro代数。然后，我们考虑由压力调整器构建的轻射运算符的换向器。使用四维CFT中光板限制的简化特征，我们提供了由特定的轻射式运算符形成的BMS代数的直接计算。在四维CFT中，我们定义了一套由应力调整构建的新型无限射线操作员，该操作器都具有明确定义的矩阵元素。这些是对二维Virasoro灯光射线算子的直接概括，这些二维灯光是从Lorentzian圆柱体中Minkowski空间的共形嵌入得出的。他们遵守与二维类似物类似的墓地条件，并共享半无限子集将真空消灭的特性。
We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.
