All Questions
Tagged with anomaly or quantum-anomalies
393 questions
101
votes
1
answer
11k
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Classical and quantum anomalies
I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view:
Anomalies are due to the fact that quantum field ...
- 6,957
54
votes
2
answers
2k
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Symmetries of the Standard Model: exact, anomalous, spontaneously broken
There are a number of possible symmetries in fundamental physics, such as:
Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and ...
- 850
38
votes
1
answer
3k
views
Instantons, anomalies, and 1-loop effects
A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way ...
- 933
30
votes
1
answer
2k
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Why do we assume local conformal transformations are symmetries in 2D CFT?
The global conformal group in 2D is $SL(2,\mathbb{C})$. It consists of the fractional linear transforms that map the Riemann sphere into itself bijectively and is finite dimensional.
However, when ...
- 2,707
29
votes
2
answers
7k
views
Central charge in a $d=2$ CFT
I've always been confused by this very VERY basic and important fact about two-dimensional CFTs. I hope I can get a satisfactory explanation here. In a classical CFT, the generators of the conformal ...
- 27.7k
29
votes
1
answer
478
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Can a theory gain symmetries through quantum corrections?
It is well known that not all symmetries are preserved when quantising a theory, as evinced by renormalising composite operators or by other means, which show that quantum corrections may alter a ...
- 739
25
votes
4
answers
8k
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Where is the Atiyah-Singer index theorem used in physics?
I'm trying to get motivated in learning the Atiyah-Singer index theorem. In most places I read about it, e.g. wikipedia, it is mentioned that the theorem is important in theoretical physics. So my ...
- 1,764
23
votes
2
answers
3k
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Why do some anomalies (only) lead to inconsistent quantum field theories
In connection with Classical and quantum anomalies, I'd like to ask for a simple explanation why some anomalies lead to valid quantum field theories while some others (happily absent in the standard ...
- 45.7k
21
votes
1
answer
808
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Quantum symmetries that are not classical symmetries
An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing ...
- 4,458
20
votes
2
answers
7k
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The phrase "Trace Anomaly" seems to be used in two different ways. What's the relation between the two?
I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing.
The first way I've seen it used is in the manner, for ...
- 3,532
19
votes
5
answers
28k
views
Why does string theory require 9 dimensions of space and one dimension of time?
String theorists say that there are many more dimensions out there, but they are too small to be detected.
However, I do not understand why there are ten dimensions and not just any other number?
...
19
votes
2
answers
6k
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What is the difference between Chiral anomaly, ABJ anomaly, and Axial anomaly?
I get confuse with these three terms: Chiral anomaly, ABJ anomaly, and Axial anomaly. I can not find standard definition of these three. Is there anyone can describe precisely?
- 199
19
votes
1
answer
3k
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What's the real resolution of the $U(1)_A$ problem?
To recap the problem, consider QCD with three massless quark flavors. There is a symmetry
$$SU(3)_L \times SU(3)_R \times U(1)_L \times U(1)_R$$
corresponding to independent rotations of the left-...
- 105k
18
votes
3
answers
2k
views
Homotopy $\pi_4(SU(2))=\mathbb{Z}_2$
Recently I read a paper using $$\pi_4(SU(2))=\mathbb{Z}_2.$$ Do you have any visualization or explanation of this result?
More generally, how do physicists understand or calculate high dimension ...
- 1,012
18
votes
2
answers
3k
views
Chiral anomalies à la Fujikawa: Why don't we just take another measure?
When deriving the chiral anomaly in the non perturbative approach for a theory of massless Dirac fermions, you start by showing that the path-integral measure is not invariant unter the chiral ...
- 481
17
votes
2
answers
2k
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How is Berry phase connected with chiral anomaly?
Recently I've read in one article about very strange way to describe chiral anomaly on quasiclassical level (i.e., on the level of Boltzmann equation and distribution function).
Starting from Weyl ...
- 8,971
17
votes
1
answer
667
views
Relation among anomaly, unitarity bound and renormalizability
There is something I'm not sure about that has come up in a comment to other question:
Why do we not have spin greater than 2?
It's a good question--- the violation of renormalizability is linked
...
- 6,957
16
votes
1
answer
2k
views
QED and anomaly
I've just started to learn anomalies in quantum field theories. I have a question.
How to show that QED is free from vector current anomaly and what would happen if it were not? In other words, how ...
- 27.2k
16
votes
2
answers
7k
views
Chiral anomaly and decay of the pion
I am told that if all classical symmetries were reflected as quantum symmetries, the decay of the neutral pion $$\pi^0 ~\longrightarrow~ \gamma\gamma$$ would not happen. Why would the conservation of ...
- 4,156
16
votes
1
answer
2k
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Why are two Higgs doublets required in SUSY?
I can't really understand why two Higgs doublets are required in SUSY.
From the literature, I have found opaque explanations that say something along the lines of: the superpotential $W$ must be a ...
- 967
16
votes
1
answer
1k
views
Conformal/trace anomaly and index theorem
I am reading the chapters on characteristic classes and the index theorems in Nakahara. It is proven in the text that any chiral or gravitational anomaly $\mathcal{A}$ is given by
$$\mathcal{A}=\int ...
- 609
15
votes
2
answers
918
views
If gauge symmetries are fake, then why do we care if they are anomalous?
My understanding is that gauge symmetries are fake in that they are only redundancies of our description of the system that we put in (either knowingly or unknowingly) see Gauge symmetry is not a ...
- 3,778
15
votes
1
answer
2k
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't Hooft vs ABJ anomalies [closed]
At some point in our physics education, we begin to accumulate a bunch of slogans related to anomalies. At some (later, in my case) point, we learn that actually there were two different kinds of ...
anon
14
votes
3
answers
3k
views
How are anomalies possible?
From Matthew D. Shwartz Quantum Field Theory textbook, he writes:
"Most of the time, a symmetry of a classical theory is also a symmetry of the quantum theory based on the same Lagrangian. When ...
- 2,740
14
votes
1
answer
2k
views
Chiral anomaly in odd spacetime dimensions
In odd number of space-time dimensions, the Fermions are not reducible (i.e. do not have left-chiral and right-chiral counterparts).
Does this mean that there is no such thing as 'chiral' anomalies ...
- 6,511
14
votes
2
answers
981
views
Can anomalies exist without gauge fields?
In Schwartz's QFT book, it is stated that anomalies cannot exist in a theory without gauge fields. This is because anomalies always give equations like
$$\partial_\mu j^\mu \sim F \tilde{F}$$
where ...
- 105k
14
votes
1
answer
840
views
Anomalies for not-on-site discrete gauge symmetries
If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
- 8,134
14
votes
2
answers
176
views
Is there a conceptual inverse of anomalies i.e. a notion of quantum enhancement of symmetries?
Anomalies usually occur when a classical symmetry ceases to be a symmetry of the theory when quantized. Are there quantum systems with certain symmetries which cease to exist when you take classical ...
- 822
13
votes
2
answers
1k
views
Is there a 2D manifold on which the Dirac equation has a zero mode?
The two-dimensional (2D) Dirac equation $(\sigma_1iD_1+\sigma_2 iD_2)\psi=E\psi$ admits zero mode ($E=0$) solutions on a non-trivial gauge background, such as the zero mode at the core of a U(1) gauge ...
- 12k
13
votes
2
answers
2k
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On the Axial Anomaly
I know that if we start with a massive theory, the chiral states $L$ and $R$ remain coupled to each other in the massless limit. Because a charged Dirac particle of a given helicity can make a ...
user12732
13
votes
1
answer
335
views
Does the Gibbons-Hawking boundary action have an anomaly inflow interpretation?
The Einstein-Hilbert action on a manifold $M$ with boundary is
$$\frac{-1}{16\pi G}\int_M d^n x \sqrt{-g} R +\frac{1}{8\pi G} \int_{\partial M} d^{n-1}x \sqrt{|h|} K$$
where $K$ is the extrinsic ...
- 2,022
12
votes
3
answers
958
views
Why is there no anomaly when particle mechanics is quantized?
We know that if one or more symmetries of the action of a classical field theory is violated in its quantized version the corresponding quantum theory is said to have anomaly.
Is this a sole feature ...
- 27.2k
12
votes
1
answer
2k
views
The index of a Dirac operator and its physical meaning
I recently read Witten's paper from the 1980s and he often uses the notion of the index of a Dirac operator in K-theory.
What is the meaning of the index of a Dirac operator?
What exactly is the ...
- 3,662
12
votes
2
answers
1k
views
Anomalies and Modification of symmetry algebra
This question is motivated by 2-dimensional CFTs where the Classical conformal group (defined by the Witt algebra) is modified to the Virasoro algebra in the quantum theory. In this question, it was ...
- 27.7k
12
votes
3
answers
971
views
Why are topological properties described by surface terms?
An example are the anomalies in abelian and non-abelian gauge quantum field theories.
For example, the abelian anomaly is $\tilde {F}_{\mu\nu}F^{\mu\nu}$ and the integral over this quantity is a ...
- 10.3k
12
votes
3
answers
1k
views
Point splitting technique in Peskin and Schroeder
One of the cornerstones of point splitting technique of calculating chiral anomaly (Peskin and Schroeder 19.1, p.655) is a symmetric limit $\epsilon \rightarrow 0$. And this is the point that I don't ...
- 885
12
votes
1
answer
929
views
Why do we solve the Wess-Zumino consistency condition using the method of descent?
Consider a quantum field theory in $d$ dimensions with a symmetry $G$. For the purpose of this discussion let's say that $d$ is even and $G$ is a compact, connected Lie group. We say that the symmetry ...
- 2,256
12
votes
2
answers
638
views
For the $U(1)$ problem, is the Kugo and Ojima Goldstone quartet wrong?
On page 96 in "Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem", Prog. Theor. Phys. Suppl. 66 (1979) 1, KO state the following:
Finally we should ...
- 161
12
votes
1
answer
1k
views
Identically vanishing trace of $T^{\mu\nu}$ and trace anomaly
Let us consider a theory defined by an action on a flat space $S[\phi]$ where $\phi$ denotes collectively the fields of the theory. We will study the theory on a general background $g_{\mu\nu}$ and ...
- 2,237
11
votes
1
answer
4k
views
What exactly is a gauge anomaly?
In lots of papers I read about gauge anomalies. For example, avoiding gauge anomalies in the MSSM is the reason for introducing an extra Higgs doublet. Gauge anomalies in the Standard Model are ...
- 519
11
votes
1
answer
2k
views
Simple explanation of chiral anomaly?
Can somebody provide a fairly brief explanation of what the chiral anomaly is? I have been unable to find a concise reference for this. I know QFT at the P&S level so don't be afraid to use math.
- 967
11
votes
1
answer
1k
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When is an anomaly one-loop exact?
There are many examples of quantum anomalies that are one-loop exact, and many examples of anomalies that have contributions to all orders in perturbation theory. I haven't been able to identify a ...
11
votes
2
answers
757
views
Why is the chiral symmetry $SU(2)_A$ not anomalous?
Using Fujikawa's path integral treatment of the triangle diagram, one can show that
$$\mathrm{Tr} \gamma^5 = \int d^4 x\ \partial_{\mu}j^{\mu} $$
Where $j^{\mu}$ is the Noether current of $U(1)_A$. ...
- 211
11
votes
3
answers
746
views
What really enforces technical naturalness of electron mass?
Technical or 't Hooft naturalness A parameter $\theta$ in the Lagrangian of a field theory is said to be natural, if in the limit of vanishing $\theta$, the theory has some enhanced symmetry. If this ...
- 27.2k
11
votes
2
answers
1k
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Parity Anomaly and Gauge Invariance
In Fermionic Path Integral and Topological Phases, Witten shows that in $2+1$ dimensions, the free massless Dirac fermion suffers from parity anomaly. To be specific, he shows that it is impossible to ...
- 2,975
11
votes
1
answer
1k
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Mathematically rather than physically speaking, is there something "special" about 10 (or 11) dimensions?
As I understand it, string theory (incorporating bosons and fermions) "works" in $9+1=10$ spacetime dimensions. In the context of dual resonance theory, I've read descriptions of why that is "...
- 457
11
votes
0
answers
223
views
Can cut-off regularisation cause a Poincaré anomaly?
Momentum cut-off regularisation leads to non-covariant results, i.e., it breaks the Poincaré covariance of the theory. Is there any guarantee that Poincaré covariance is always restored when we remove ...
10
votes
2
answers
904
views
How is the pion related to spontaneous symmetry breaking in QCD?
In chapter 19 of An Introduction to Quantum Field Theory by Peskin & Schroeder, they discuss spontaneous symmetry breaking (SSB) at low energies in massless (or nearly massless) QCD, given by
$$\...
- 111
10
votes
2
answers
4k
views
Anomalies in QFT
I am a first year PhD student in theoretical physics with a background in QFT (up until relativistic fields, path integrals and gauge theories and anomalies) and some algebraic topology but my ...
10
votes
1
answer
2k
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Chiral anomalies
Recently I have read that there is contraction of chiral anomalies in SM. But people are working on chiral anomalies theory. So I have the question: what is the importance of development of the theory ...
- 6,632