All Questions
Tagged with anomaly or quantum-anomalies
82 questions
101
votes
1
answer
11k
views
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
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?
...
8
votes
1
answer
2k
views
How to calculate an axial anomaly in 1+1 dimensions?
As far as I understand, an axial $U(1)$ transformation transforms a two-component spinor like
$$ \psi \to \psi'=\text e^{\text i\epsilon \gamma^5 }\psi,\qquad \psi=\begin{pmatrix}\psi_1\\\psi_2\end{...
- 2,678
16
votes
2
answers
7k
views
Chiral anomaly and decay of the pion
I am told that if all classical symmetries were reflected as quantum symmetries, the decay of the neutral pion $$\pi^0 ~\longrightarrow~ \gamma\gamma$$ would not happen. Why would the conservation of ...
- 4,156
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
23
votes
2
answers
3k
views
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
8
votes
2
answers
3k
views
Weyl anomaly in 2d CFT (string theory lectures by D.Tong)
In his lectures on String Theory (http://www.damtp.cam.ac.uk/user/tong/string.html), Tong gives a proof of the Weyl anomaly, using equation $(4.37)$. It seems wrong to me.
Here he uses the OPE between ...
- 116
11
votes
1
answer
1k
views
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
5
votes
1
answer
318
views
Can the effective vertex for $\gamma\to3\pi$ be derived directly from the anomaly?
My question is whether the effective vertex for $\gamma\to3\pi$ can be derived directly from the anomaly (given in the first equation below), in analogy with the $\pi^0\to2\gamma$ vertex? As far as I ...
- 1,594
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
6
votes
1
answer
4k
views
Anomaly cancellation in the standard model (calculating the symmetrized trace of generators)
The Problem
We can show that the condition for the Standard Model to be anomaly-free is that the symmetrized trace over the generators of the gauge group vanishes:
\begin{align}
\text{tr} \big(\{\...
- 261
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 ...
9
votes
2
answers
1k
views
Choice of basis for Fujikawa method to derive chiral anomaly
I am studying the Fujikawa method of determining the chiral anomalies in a $U(1)$ theory. As we know the basis vectors selected are the eigenstates of the Dirac operator. One of the reasons given is ...
- 311
8
votes
1
answer
1k
views
Why is baryon or lepton violation in standard model is a non-perturbative effect?
The baryon number B or lepton number L violation in the standard model arise from triangle anomaly. Right? Triangle diagrams are perturbative diagrams. Then why the B or L violation in Standard model ...
- 27.2k
5
votes
1
answer
3k
views
Baryon number violation in the Standard Model
Anomaly cancellation in the Standard model requires $B-L$ to be constant, which is done using perturbative diagrammatic expansion. Secondly, baryon number is conserved as an $U(1)$ global field ...
- 5,287
3
votes
3
answers
1k
views
Question on Conformal Field Theory
Since every question has to be asked in a seperate topic,
I'm asking a question refering to the following topic:
Beginners questions concerning Conformal Field Theory
In particular I'm referring to ...
- 391
1
vote
1
answer
337
views
Axial anomaly at the level of particles
Consider pure QED with massless electrons. Due to the axial anomaly the axial current is not conserved:
$$
\tag 1 \partial_{\mu}J^{\mu}_{5} \sim F_{\mu\nu}\tilde{F}^{\mu\nu}
$$
On the other hand, it ...
- 8,971
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
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
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
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
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
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 ...
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
9
votes
2
answers
503
views
Quantum Anomalies and Quantum Symmetries
In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be ...
- 175
9
votes
1
answer
523
views
How projective representations can lead to 't Hooft anomalies in quantum mechanics?
In Shao's talk https://youtu.be/2vTvHYYl1Qk?t=1554, he argues that in quantum mechanics "if a symmetry acts projectively on states, then we have a t' Hooft anomaly". But I'm having trouble ...
- 471
8
votes
1
answer
842
views
About the general expression of trace anomaly and CFT partition functions
I have put up a question here,
https://mathoverflow.net/questions/139685/proof-of-the-general-expression-for-anomaly-in-a-cft-and-its-partition-function
Here I am putting up a slightly different ...
- 4,709
5
votes
2
answers
2k
views
How exactly do superstrings reduce the number of dimensions in bosonic string theory from 26 to 10 and remove the tachyons?
In bosonic string theory, to obtain the photon as the first excited state, the ground state must have a negative mass (tachyon). By applying $1 + 2 + 3 + \cdots = -1/12$, it can be shown (in a ...
- 9,691
4
votes
1
answer
326
views
What does $B+L$ anomaly have to do with a phase redefinition of the left-handed quark field?
According to this answer, the reason why $SU(2)_L$ weak theory does not have a theta vacuum is because any theta term can be reabsorbed with a phase redefinition of the left-handed quark field.
...
- 2,646
3
votes
1
answer
674
views
Hermiticity of Dirac Operator $\gamma^{\mu}D_{\mu}$ and Expansion in eigenmodes
I'm interested to know under what conditions $\gamma^{\mu}D_{\mu}$ is a hermitian operator.
I am studying the Fujikawa method of anomalies and I see that many sources have different answers for this. ...
- 2,816
3
votes
1
answer
8k
views
Why are there specifically 10, 11, or 26 dimensions in string theory? [duplicate]
I know that current string theories state that there are 10, 11, or 26 spacetime dimensions in superstring theory, M-theory, and bosonic string theory, respectively. But when I looked up why those ...
1
vote
0
answers
346
views
The locality of Wess-Zumino terms
Suppose the simple theory with chiral fermions possessing non-trivial gauge anomalies cancellation:
$$
S = \int d^4 x \big(\bar{\psi}i\gamma_{\mu}D^{\mu}_{\psi}\psi + \bar{\kappa}i\gamma_{\mu}D^{\mu}_{...
- 8,971
30
votes
1
answer
2k
views
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
25
votes
4
answers
8k
views
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
21
votes
1
answer
808
views
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
19
votes
1
answer
3k
views
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
17
votes
2
answers
2k
views
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
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
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
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
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
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
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
1k
views
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 ...
10
votes
1
answer
709
views
Theta Vacuum of Yang-Mills theory and Baryon number violation
Background 1. In classical SU(N) Yang-Mills theories, there are a countably infinite number of homotopically inequivalent gauge field configurations of zero energy labelled by a winding number $n\in \...
- 27.2k
8
votes
1
answer
1k
views
How should we think of local counterterms in the context of anomalies?
Short version: effective actions, particularly ones obtained after integrating chiral fermions, are ambiguous up to the addition of local counterterms. Should we think of the counterterms as part of ...
- 451
8
votes
1
answer
575
views
Nielsen-Ninomiya Theorem versus Chiral Gauge Anomaly
As far as I understand, the Nielsen-Ninomiya theorem states that (under mild conditions) the number of left and right-handed chiral fermions must be equal on the lattice, while the chiral gauge ...
- 2,989
8
votes
2
answers
849
views
Does the Coleman-Weinberg mechanism belong to the dynamical symmetry breaking or the anomaly?
We know that a massless $\phi^4$ theory
$$S=\int d^4x \left[\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{\lambda}{4!}\phi^4\right],$$
has conformal invariance at the classical level. But within ...
- 3,741
8
votes
1
answer
1k
views
Zumino's consistent and covariant anomalies - applied to quantum hall?
What is the `physical' meaning of consistent anomalies and covariant anomalies?
Perhaps a good Reference is:
Consistent and covariant anomalies in gauge and gravitational theories -
William A. ...
- 7,928