标题： 共形对称性真的存在反常吗？ 显示英文标题

标题： Is conformal symmetry really anomalous?

摘要： 共形异常（也称为应力-能量迹异常）是相互作用量子理论中与量子效应对Weyl（共形）对称性的破坏有关的异常，如果将该理论赋予一个与矢量场耦合的尺度电流，而该矢量场是局部Weyl对称变换的规范连接，则可以修正这种异常。 这个Weyl连接的自然候选是几何扭力张量的迹，特别是当人们回忆起带有扭力的纯（Cartan-Einstein）引力是共形的时候。 我们首先指出，规范和路径积分量化都尊重Weyl对称性。 量子效应唯一可能破坏共形对称性的方式是通过正则化过程。 然而，如果通过使用与Weyl对称性一致的正则化程序从一个共形不变的经典理论计算有效作用量，则共形Ward恒等式将被满足。 从这个意义上说，Weyl对称性不会被量子效应破坏。 这项工作表明，Weyl对称性可以与规范对称性和引力同等对待，对于这些对称性，无限组的Ward恒等式保证它们不会被量子效应破坏。 显示英文摘要

摘要： The conformal anomaly (also known as the stress-energy trace anomaly) of an interacting quantum theory, associated with violation of Weyl (conformal) symmetry by quantum effects, can be amended if one endows the theory with a dilatation current coupled to a vector field that is the gauge connection of local Weyl symmetry transformations. The natural candidate for this Weyl connection is the trace of the geometric torsion tensor, especially if one recalls that pure (Cartan-Einstein) gravity with torsion is conformal. We first point out that both canonical and path integral quantisation respect Weyl symmetry. The only way quantum effects can violate conformal symmetry is by the process of regularization. However, if one calculates an effective action from a conformally invariant classical theory by using a regularisation procedure that is conform with Weyl symmetry, then the conformal Ward identities will be satisfied. In this sense Weyl symmetry is not broken by quantum effects. This work suggests that Weyl symmetry can be treated on equal footing with gauge symmetries and gravity, for which an infinite set of Ward identities guarantees that they remain unbroken by quantum effects.