All Questions
Tagged with anomaly or quantum-anomalies
393 questions
5
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0
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113
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New symmetries upon quantization
In standard field theory texts, a “classical symmetry” is defined to be a transformation $\phi\to\phi’$ such that the corresponding action is left invariant. The symmetry is said to survive ...
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1
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0
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60
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Standard model extension
this Semester I have my first QFT class and we have a homework where I got stuck at the beginning.
I have some ideas but I am not sure if they are correct, so I don't want a solution, I only want to ...
- 11
3
votes
1
answer
207
views
Weinberg Volume II: Abelian Anomaly Function
The following is from page 363 of Weinberg volume II.
We wish to evaluate the RHS of
\begin{align}\label{EQbbvbv}
[d \psi][d \bar{\psi}] \rightarrow(\operatorname{Det} \mathscr{U} \operatorname{Det}...
- 321
0
votes
0
answers
67
views
Critical dimension from the symmetries of the string action
(Related: This post and this post.)
In this thesis it is said (on page 13) that just by assuming that we have some general action with the same symmetries as the Polyakov action (Poincare invariance, ...
- 817
5
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0
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157
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Factor of 2 issue in the non-gauge invariance of Chern-Simons theory with a boundary
It is well known that the Chern-Simons (CS) theory by itself is not gauge invariant in the presence of a spacetime boundary. Concretely, suppose the flat half space $\mathcal{M}$ with $x\in \mathbb{R},...
- 1,515
3
votes
1
answer
318
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How to prove that a given correlation function is protected?
I would be interested in proving that $2$-point functions made of $1/2$-BPS operators are protected in $\mathcal{N}=4$ SYM (Supersymmetric Yang-Mills), i.e. that the correlator $\langle \mathcal{O}_2(...
- 1,743
2
votes
1
answer
558
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Peskin's treatment of Pions as Goldstone Bosons
After restoring the mass terms in the Lagrangian
\begin{align}
\mathcal{L}=\bar{u} i \not D u+\bar{d i} \not D d-m_{u} \bar{u} u-m_{d} \bar{d} d,
\end{align}
one obtains equations of motion for the ...
- 321
2
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0
answers
220
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Chiral anomaly: gauge covariance and regularization
I am looking at the treatment of the chiral anomaly in Fujikawa and Suzuki's "Path Integrals and Quantum Anomalies." To illustrate the quantum breaking of chiral symmetry (section 4.3), they start ...
- 321
2
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0
answers
341
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Is there a way to make this simple "derivation" of the Trace Anomaly correct?
I think I came up with a simple yet sketchy almost-proof of the trace anomaly (A.K.A. Weyl anomaly) in 2D CFT, but it has the wrong prefactor. I was wondering if anyone could assess whether this "...
- 11.8k
1
vote
1
answer
293
views
Gauge anomaly in Polyakov string and Faddeev-Popov method
I am currently trying to gain a better understanding of the gauge fixing procedure used in chapter 5 of David Tong's notes.
Since the central charge of the Polyakov action for, say, the bosonic ...
- 261
4
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0
answers
92
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Anomalies depend on how they are calculated. How is this satisfactory?
If we have a set of linear symmetry currents $J^{\mu}_{\alpha}$ and attempt to find if they are anomalous, we find that if we change the regularization procedure, the anomaly will get mixed around the ...
- 3,544
4
votes
1
answer
162
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Momentum replacement in the axial anomaly calculation in dimensional regularisation (‘t Hooft prescription)
I have been studying the axial anomaly and everywhere I see the calculation of the triangle loop using dimensional regularisation (see for example pages 661-664 of section 19.2 of Peskin). In the ‘t ...
2
votes
1
answer
408
views
Anomaly vs spontaneous symmetry breaking
I was trying to gain a basic understanding of anomalies. In the case of anomalies, certain correlations which should have been zero based on symmetry considerations of the action, instead turn out to ...
- 978
7
votes
1
answer
208
views
Time-reversal (explicitly) broken surface of $(3+1)$-dimensional topological insulator
Let us consider the surface of $(3+1)$-dimensional topological insulator, which is protected by the charge conservation $U(1)_Q$ and a time-reversal symmetry $\mathbb{Z}_2^T$. Such a surface, if not ...
- 823
2
votes
0
answers
166
views
Exotic perturbative anomaly captured only by higher-loop Feynman graphs, but not by any 1-loop Feynman graph?
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 ...
- 4,376
2
votes
1
answer
101
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Anomalies in Global Symmetries (Srednicki ch 76)
In chapter 76 of Srednicki's QFT book, he defines $C^{\mu\nu\rho}(p,q,r)$ via (76.21)
\begin{equation}
(2\pi)^{4}\delta^{4}(p+q+r)C^{\mu\nu\rho}(p,q,r)\equiv \int d^{4}xd^{4}yd^{4}z e^{-i(px+qy+rz)}\...
- 35
8
votes
0
answers
355
views
How is group cohomology in SPT's related to the 't Hooft anomaly on the boundary?
I understand that group cohomology description for symmetry protected topological phases (SPT) comes from discrete nonlinear sigma models. A tutorial on this can be found in the excellent lectures by ...
- 1,515
6
votes
2
answers
329
views
Particle on a circle with magnetic flux$.$
I am trying to understand the model studied in 1905.09315 §2, to wit, a $0+1$ dimensional theory with target space $\mathbb S^1$ with non-trivial magnetic flux:
$$
\mathcal L=\frac12m\dot q^2-\frac{i}{...
7
votes
1
answer
2k
views
Why does a triangle anomaly appear in a gauge theory?
I have read that when we construct a theory with abelian gauge symmetry there will appear some anomalies when we do the quantum correction to the theory. In 4D space such anomalies are explained by ...
- 157
1
vote
0
answers
103
views
Higher point anomalies cancellation from trace
I had asked this question within this one before, but having also made other 2 independent enough questions there, decided to ask this one by itself here.
So, it is a well known fact that the ...
- 1,782
0
votes
1
answer
87
views
Nuclei violating B number
Within SM, it is know that baryon number is not preserved and changes as
$$
\Delta B = 3·\Delta n_{CS}, \quad n_{CS} \in \mathbb{Z}\ ({\rm Chern-Simons\ index\ for\ vacuum})
\tag1$$
Then, its ...
- 1,607
0
votes
0
answers
60
views
B violation and electric charge
Within SM you can prove that despite we have baryon number conservation respect to Noether theorem, at quantum level baryon (and lepton) number is violated as
$$
\Delta B = 3·\Delta n_{CS}, \quad n_{...
- 1,607
1
vote
1
answer
281
views
Is string theory self-consistent? (Conformal anomaly)
Recently I attended a very short course on string theory. We went through the standard presentation in light-cone gauge for brevity. We ‘derived’ the Einstein field equation in the following manner. ...
- 526
1
vote
0
answers
212
views
Diagrammatic expansion of an operator insertion in path integral for Trace Anomaly calculation
Starting with a scale invariant classical field theory, we can prove that the energy-momentum tensor will be traceless.
\begin{equation}
\Theta^\mu_{\ \mu }=0
\end{equation}
In the context of the ...
- 4,737
5
votes
2
answers
1k
views
Relation between the trace anomaly and the energy-momentum tensor being off-shell
Let's say we have a massless QED theory with a Lagrangian
\begin{equation}
L=i\bar{\psi}\not{D}\psi-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}
\end{equation}
The symmetric energy-momentum tensor is
\begin{...
- 4,737
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
7
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0
answers
411
views
Ward identity for 'general' operator and current diagrams
This is actually about two related doubts and I hope is appropriate for a single question (if not, I will happily divide it). So, my problems are related to the analysis and calculation of chiral ...
- 1,782
0
votes
0
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234
views
Peskin equation on the treatment of chiral anomaly
In page 666 (it couldn't be other way - bad joke), chapter 19, the Eq. (19.73) claims (see properties of the $\phi_n(x)$ functions in this post: Change of variables in path integral measure):
$$
\...
- 1,607
0
votes
0
answers
424
views
QCD Trace Anomaly and Mass
In the paper in equations 4 and 5, some of the mass of the nucleons comes from the "trace anomaly" of the QCD energy-momentum tensor (as described in the paragraph following these equations). Is there ...
- 1
7
votes
2
answers
527
views
How do anomalies affect the field equations of motion?
I find anomalies an extremely unintuitive subject, because they're studied so indirectly. In the standard textbook presentation, one computes an abstract quantity that should be zero classically (say, ...
- 105k
4
votes
0
answers
312
views
How does the Weyl anomaly imply $\langle T^{\mu}_{\mu} \rangle \neq 0$?
I want to consider the case of euclidean field theory in 2 dimensions with the action
$$S[\phi]=\int \! d^2\!x \sqrt{\det(g)}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$$
which leads to a partition ...
- 261
8
votes
1
answer
558
views
Does the massless fermion in $2+1$ dimensions suffer from gauge anomaly?
In Fermion Path Integrals And Topological Phases Witten showed that for a massless Dirac fermion in $2+1$ dimensions
$$S[\bar{\psi},\psi]=\int d^{3}x\bar{\psi}iD\!\!\!\!/_{A}\psi,$$
where $A$ is a $...
- 2,975
3
votes
1
answer
394
views
Does the vanishing of the one-loop beta-function imply no running to all orders?
This question sounds ridiculous, but bear with me. I am having a hard time reconciling the following two facts:
Classical global symmetries can become anomalous upon quantization, and the anomalous ...
- 8,582
8
votes
1
answer
246
views
Viewing anomalous dimensions in RG as a quantum anomaly
Other than sharing the word “anomalous”, both the anomalous dimension in RG and the more well-known quantum anomalies (such as chiral anomaly) share a common feature. These are violations of classical ...
- 1,515
2
votes
1
answer
118
views
In the case of the Dirac Equation,what forbids the free electron to absorb a photon? (electron magnetic moment)
It is straightforward to show from relativistic kinematics that a free electron cannot absorb a photon, as shown in this previous thread.
However, It is also known that using the Dirac equation, you ...
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
9
votes
1
answer
717
views
Anomaly is due to the noninvariance of the path-integral under a symmetry. Is the noninvariance reflected on 1PI effective action?
When a symmetry is anomalous, the path integral $Z=\int\mathcal{D}\phi e^{iS[\phi]}$ is not invariant under that group of symmetry transformations $G$. This is because though the classical action $S[\...
- 27.2k
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
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
2
votes
0
answers
365
views
Why Parity Anomaly in Odd Dimensions?
In section 13.6 of Nakahara, the parity anomaly is in odd dimensional spacetime.
From the paper Fermionic Path Integral And Topological Phases by Witten, the problem appears as one cannot define the ...
- 2,975
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 ...
7
votes
2
answers
666
views
APS $\eta$-invariant and spin-Ising TQFT
I am interested in the relation between the Atiyah-Patodi-Singer-$\eta$ invariant and spin topological quantum field theory. In the paper Gapped Boundary Phases of Topological Insulators via Weak ...
- 2,975
1
vote
1
answer
201
views
How does the global $G^2G'$ anomaly make all the $\theta$-vacua associated to the gauge group $G$ physically equivalent?
Consider a gauge group $G$ and suppose that there is a $\theta$-term associated to it. According to this answer, the existence of a global anomalous symmetry $G'$ which rotates the $\theta$-term, ...
- 2,646
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
4
votes
1
answer
373
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"The operators with nontrivial vacuum expectation values have to soak up the zero modes associated to the anomaly."
I was reading ref.1, where one can read (emphasis mine)
... the vacuum expectation value $\langle \mathcal O_{\phi_1}\cdots \mathcal O_{\phi_\ell}\rangle$ vanishes unless
$$
\sum_{k=1}^\ell\...
5
votes
1
answer
368
views
What is the physical interpretation of chirality / chiral anomaly?
I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What ...
- 151
2
votes
1
answer
236
views
Are anomalies always undesirable?
In the glossary of the AMS book on Quantum Fields and Strings it is stated that
An anomalous theory does not make sense quantum mechanically, so anomaly cancellation is a fundamental requirement ...
- 9,444
5
votes
0
answers
210
views
Is it possible to couple an odd number of Dirac fermions, at finite density, to a massless gauge field in 2+1d?
In a beautiful paper by A. N. Redlich (PRL $\bf{52}$, 18 (1984)) on the parity anomaly, the author indicates that an odd number of Dirac fermions can never be coupled to a massless gauge field in 2+1d ...
- 51
1
vote
0
answers
86
views
Trouble Understanding Computation in Weinberg Quantum Theory of Fields Vol. 2 Chapter 22
In Chapter 22 (Anomalies) of Weinberg Vol. 2, the author is evaluating the anomaly function
$\mathcal{A}(x) = -2[Tr(\gamma_5 t f(-(\not{D}/M)^2))\delta(x-y)]_{y\rightarrow x}$,
following Fujikawa'...
- 739
1
vote
0
answers
76
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Showing that $U(1)_R$ charge is non-anomalous in SUSY QCD when $r=\frac{F-N}{F}$
I'm trying to show that the value of the R-charge $r$ for which the R-symmetry is non-anomalous is given by $r=\frac{F-N}{F}$.
To do this we must calculate the triangle diagrams for the quarks $\...
- 4,820