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Diffeomorphism invariance demands conformal anomalies

机译：Diffeomorphism Invariance要求共形异常

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We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make nonlocal loop correction terms diffeomorphism invariant. Specifically, in a conformally flat spacetime d s 2 = e 2 ? ( ? d η 2 + d x 2 ) , we find that effective actions are described in terms of momentum squared expressed as a physical Q 2 = q 2 / e 2 ? for q 2 measured by the flat metric, which recalls the relationship between physical momentum and comoving momentum in cosmology. It is confirmed by calculating the effective action of QED in such a curved spacetime at the 3-loop level using dimensional regularization. The same applies to the case of QCD, in which we show that the effective action can be summarized in the form of the reciprocal of a running coupling constant squared described by the physical momentum. We also see that the same holds for renormalizable quantum conformal gravity and that conformal anomalies are indispensable for formulating the theory.
机译：我们研究了一系列通过反复积分关于在较高循环处出现的共形因子场的共形异常而获得的WESS-Zumino动作。我们表明它们出现为使非局部循环校正术语扩散不变所需的物理量。具体地，在一个共形平坦的时空D S 2 = E 2中？ （？Dη2+ d x 2），我们发现，根据表示物理q 2 = q 2 / e 2表示的动量方形描述有效行动？对于通过平度量测量的Q 2，这回顾了物理动量与宇宙中的动量之间的关系。通过使用尺寸正则化计算在3环水平的这种弯曲时空中的QED的有效作用来确认。这同样适用于QCD的情况，在其中我们表明可以以物理动量描述的运行耦合恒定平方的倒数的形式总结有效动作。我们还看到相同的持有对重型化量子保形重力以及共形异常是必不可少的，用于制定理论。

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