Talk:Anomaly (physics)

Anomaly category

There seem to already been a lot of anomaly articles. This one, the descriptions of the individual anomalies, articles on index theorems and BRST techniques that calculate anomalies, articles on anomaly-cancellation mechanisms, etc. And some are conspicuously missing (an article on the Wess-Zumino consistency condition, the Konishi anomaly, the Freed-Witten anomaly, the U(1)_R anomaly, etc.) Maybe an anomaly category should be created? JarahE 21:36, 26 April 2006 (UTC)

Long/short distance effect section is dubious

Anomalous symmetry is simply not a symmetry of the quantum theory, so in what sense is it a UV or IR effect? Furthermore, in cases where such a meaning can be given, it seems odd to claim that this is an IR effect:

• In the specific case of scale-invariance anomaly of QCD, which indeed can have such an interpretation, it is thought to arise as an effect of having an underlying scale (GUT scale or planck scale - remember one has the coupling at this scale, and letting the coupling run as the energy gets lower, one gets $\Lambda _{QCD}$ as the limit where this coupling diverges) - thus it is a UV effect rather than an IR one.
• In the case of a chiral anomaly, non-conservation happens in nature as a result of an instaton effect, which is an IR effect. However the non-conservation comes from the UV degrees of freedom. For example, in the case of non-conservation of particle number, fermions appear from the fermi sea due to energy level shift, and can be thought of as coming from the depth of sea fermi, i.e. from the UV (depth of sea fermi -> energy -infinity -> UV effect) - see for example Peskin, chapter 19.1.

If no citation appears in reasonable time, I will delete the whole section, or replace it by the discussion I have just wrote, unless I get a reasonable answer for my doubts.

I have also omitted the "massless or nearly massless particle" part, since there is no such particle in the anomalies I am aware of in nature (scale-invariance anomaly of QCD, chiral anomaly - this causes eta to have a large mass, while the pion has a low mass because its corresponding symmetry is non-anomalous, baryon number anomaly etc.). It seems the author has been confused by the appearance of the goldstone boson in the case of a spontaniously broken symmetry. Dan Gluck 16:35, 2 May 2007 (UTC)

You ask "in what sense is it a UV or IR effect?". An example of violation of symmetry (example that is not an anomaly) that is coming from the UV is lepton number. Lepton number is conserved to a very good approximation because it is violated only by higher-dimensional operators which are suppressed by a large mass scale (maybe GUT scale or Planck scale). If this mass scale is taken to infinity, the symmetry becomes exact. Thus, lepton number violation by higher dimensional operators is a UV effect, that depends on the physics out there at the cutoff. Anomaly is not only a UV effect (appears from the inability to regularize the infinities in a way that is consistent with the symmetry) but also an IR effect (can be derived even without considering UV divergences; does not disappear when the energy scale of the UV physics is taken to infinity).

By the way, $\Lambda _{QCD}$ doesn't have anything to do with GUT scale or Planck scale. The coupling would be running even if the theory were valid to arbitrarily large energy scales.

As for the "massless particles" sentence, it originated here (by Lubos Motl) as something correct, and was taken out of context later on. Yevgeny Kats 00:24, 6 May 2007 (UTC)

My point was that anomaly is not an effect of the UV or IR, it is rather a property of the theory. Indeed 't Hooft showed that the anomalies in IR degrees of freedom and UV degrees of freedom are the same. For anomalies of global currents, there is no "danger" in the anomaly, it is just that there is a transformation which is not a symmetry, even though classically it looks like one. Regarding anomalies of local currents (gauge symmetries), they are not "dangerous more than non-renormalizability", they are simply inconsistent, and surely they cannot be called IR or UV effect since they simply must not exist. The fact that "in general anomalies are determined entirely by the quantum numbers of the elementary fields" does not imply that they are IR effect, and in fact as 't Hooft showed one can look either at the fields in the UV (i.e. the "elementary" ones in the proper sense) or at the IR and get the same result, if the symmetry can be defined for both cases.Moreover, in far IR, in the proper sense, there are only massless fields, which means that in nature we only have a theory of free photons (and possibly one type of neutrino, non-interacting in the IR limit) and there is no sense to speak of anomalies. Regarding $\Lambda _{QCD}$, it is true that there must appear a scale even with a theory that is UV complete, but we do know that there should be some UV completion, which has a natural scale such as the planck mass, and in this UV completion we get $\Lambda _{QCD}$ is $exp(-C/g(M)^{2})$, from the running of coupling, where C is some constant and g(M) is the coupling at the energy scale where the new UV physics appears. In fact this is a way to understand why $\Lambda _{QCD}\ll M_{planck}$ (see for example the 45-46th minute at Gross's lecture. Dan Gluck 14:27, 6 May 2007 (UTC)

By the way it seems to me that you are confusing lepton number anomaly of the Standard Model and higher-dimensional lepton number violating terms in the GUT Lagrangian. These are two different effects. Remember an anomalous symmetry is a symmetry of the Lagrangian but not of the measure. Dan Gluck 14:31, 6 May 2007 (UTC)

I agree with you that the section is not perfect (and I wasn't the one who wrote it). I just wanted to point out that it's not a complete nonsense as you first suggested. Feel free to correct it.

As to whether it's useful or not to say that anomalies are "UV and IR effect", I can just tell you from my own experience that some people do use this kind of terminology.

I am not confusing lepton number anomaly with higher-dimensional terms. I didn't say a word about lepton number anomaly. (By the way, the higher dimensional terms do not come necessarily from the GUT Lagrangian.) Yevgeny Kats 14:56, 6 May 2007 (UTC)

OK I corrected the section (and changed it's name), hope it's also to your taste now. Dan Gluck 15:04, 6 May 2007 (UTC)

I would just add that in general anomalies tend to be sort of BOTH IR and UV effects. They typically arise because the UV regulator violates a symmetry, but the obstruction to the regulator preserving the symmetry is topological, or IR.PhysPhD 18:03, 19 May 2007 (UTC)

Is this true?

"note that all the anomaly cancellation mechanisms result in a spontaneous symmetry breaking of the symmetry whose anomaly is being cancelled."PhysPhD 18:26, 19 May 2007 (UTC)

No. Removed it. Cuzkatzimhut (talk) 00:49, 26 April 2017 (UTC)

Gauge anomalies

This section mentions boson loops where I think fermion loops would be appropriate, as depicted in the gauge anomaly article. What do you think? Wferi (talk) 18:43, 19 February 2008 (UTC)

Turbulence

Perhaps, the first known anomaly was the dissipative anomaly in turbulence: time-reversibility
remains broken (and energy dissipation rate finite) at the limit of vanishing viscosity.

In which order are the limits taken??? AnonyScientist (talk) 07:48, 27 March 2008 (UTC)

Seems there's only one limit taken: zero viscosity. —Preceding unsigned comment added by PhysPhD (talk • contribs) 14:10, 27 March 2008 (UTC)

Anomaly Cancellation

I don't think the stated condition suffices to conclude that the electron and proton charge cancel. For example, on p. 101 in The Standard Model: A Primer, they also use the cancellation of the diagram with three U(1) generators and the neutrality of the Yukawa terms. Valentinwust (talk) 20:17, 14 April 2020 (UTC)