Exotic perturbative anomaly captured only by higher-loop Feynman graphs, but not by any 1-loop Feynman graph?

Asked Jun 28 '19 at 04:28

Active Jun 28 '19 at 04:28

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My question: Are there any perturbative anomaly captured by higher-loop but not by captured at the 1-loop Feynman graph (say, not enough)?

We are familiar with the text book example of a perturbative anomaly captured by 1-loop Feynman graph, such as the ABJ anomaly.

All anomalies in Green-Schwarz mechanism are also perturbative anomaly captured by 1-loop Feynman graphs. I also know global anomalies of Witten SU(2) and global gravitational anomalies not captured by perturbative Feynman graphs.

My question: Are there any perturbative anomaly captured by higher-loop but not by captured at the 1-loop Feynman graph (say, not enough)?

asked Jun 28 '19 at 04:28

ann marie cœur

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In a large class of theories, the Adler-Bardeen theorem, which states that if anomalies vanish at one loop, then they vanish to all orders, has been proved to hold. – MannyC Jun 28 '19 at 05:49
possible dup.? When is an anomaly one-loop exact?. – AccidentalFourierTransform Jun 28 '19 at 14:22
I am asking beyond 1-loop, thus it is not a duplicated question -- please do not limit the imagination. – ann marie cœur Jun 28 '19 at 16:30

Exotic perturbative anomaly captured only by higher-loop Feynman graphs, but not by any 1-loop Feynman graph?

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