Gauge anomalies (and cancellations)

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In summary, the conversation discusses the difficulty in understanding gauge anomalies and cancellations in the context of perturbative and nonperturbative phenomena. The concept of "anomalous" symmetry is explained as a symmetry that exists in the classical model but not in the quantum model. The conversation also touches on the idea of studying this system on a lattice and its implications on symmetry.
  • #1
diegzumillo
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Hey all
As usual I can get through the specifics of calculations on books but the big picture escapes me. I'm having difficulty understanding gauge anomalies and cancellations. To be more specific, every book I read talks about Feynman diagrams, giving the impression that gauge anomalies are a perturbative phenomena. On the other hand, the anomaly seems to come from a symmetry of the lagrangian on chiral theories, and I don't see anything perturbation-specific there.

I'd appreciate any help, indlucing some interesting references on the subject.
 
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  • #2
The point is that an "anomalous" symmetry is a symmetry which is a symmetry of the classical model but not of the quantum model. So nonperturbatively, you won't see any symmetry at all.
 
  • #3
Just to be clear. When you say classical model and quantum you are referring to the Lagrangian symmetries and the usual quantization procedures, or equivalently tree-level and higher order diagrams, right? And in a hypothetical scenario, if we could study this system in, say, a lattice there would be no symmetry to be broken in the first place.
 

What are gauge anomalies?

Gauge anomalies are quantum mechanical effects that arise in the study of gauge theories. They are deviations from classical symmetries that can occur when attempting to quantize a theory with a gauge symmetry.

Why are gauge anomalies important?

Gauge anomalies are important because they can lead to inconsistencies in the theory, such as non-unitarity and non-renormalizability. They also have implications for the physical predictions of the theory, as they can affect the behavior of particles and interactions.

How are gauge anomalies detected?

Gauge anomalies can be detected through the use of Ward identities, which are equations that relate different physical observables in a gauge theory. If the Ward identities are violated, it is a sign that a gauge anomaly is present.

Can gauge anomalies be cancelled?

Yes, gauge anomalies can be cancelled by adding new particles to the theory or by choosing the gauge group and representation carefully. This cancellation is necessary for the consistency of the theory.

What is the significance of gauge anomaly cancellations?

The cancellation of gauge anomalies is significant because it ensures that the theory is consistent and that physical predictions can be made without encountering any inconsistencies. It also provides insight into the underlying symmetries and structure of the theory.

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