Questions tagged [quantum-anomalies]
This tag is for anomalies in a symmetry, either in classical or quantum theories. DO NOT USE THIS TAG for anomalies in a measurement.
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0answers
20 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
votes
0answers
26 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{...
10
votes
3answers
278 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 ...
4
votes
0answers
166 views
Ward identity for 'general' operator, higher point anomalies cancellation and current diagrams
This is actually about several 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 ...
0
votes
0answers
69 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):
$$
\...
0
votes
0answers
27 views
References to understand BRST Quantization
I'm looking for good, rigorous references that discuss BRST quantization in relation to how it leads to dealing with anomalies and ghost fields. I'm looking at high level references (i.e., assume ...
0
votes
0answers
31 views
QCD Trace Anomaly and Mass
In the paper in equations 4 and 5, some of the mass of the nucleons comes from the "trace anomaly" of the QCD energy-momentum tensor (as described in the paragraph following these equations). Is there ...
5
votes
2answers
237 views
How do anomalies affect the field equations of motion?
I find anomalies an extremely unintuitive subject, because they're studied so indirectly. In the standard textbook presentation, one computes an abstract quantity that should be zero classically (say, ...
2
votes
0answers
36 views
How does the Weyl anomaly imply $\langle T^{\mu}_{\mu} \rangle \neq 0$
I want to consider the case of euclidean field theory in 2 dimensions with the action
$$S[\phi]=\int \! d^2\!x \sqrt{\det(g)}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$$
which leads to a partition ...
3
votes
1answer
72 views
Does the massless fermion in $2+1$ dimensions suffer from gauge anomaly?
In Fermion Path Integrals And Topological Phases Witten showed that for a massless Dirac fermion in $2+1$ dimensions
$$S[\bar{\psi},\psi]=\int d^{3}x\bar{\psi}iD\!\!\!\!/_{A}\psi,$$
where $A$ is a $...
2
votes
1answer
84 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 ...
5
votes
1answer
67 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 ...
2
votes
1answer
42 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 ...
6
votes
2answers
259 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 $(4.36)$. It seems wrong to me.
Here he uses the OPE ...
7
votes
1answer
148 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[\...
5
votes
0answers
85 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 ...
6
votes
2answers
170 views
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 ...
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0answers
98 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 ...
7
votes
1answer
160 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 ...
5
votes
2answers
130 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 ...
1
vote
1answer
57 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, ...
1
vote
1answer
91 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.
...
5
votes
1answer
98 views
“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\...
3
votes
1answer
151 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 ...
1
vote
1answer
107 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 ...
5
votes
0answers
132 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 ...
1
vote
0answers
37 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'...
1
vote
0answers
41 views
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 $\...
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0answers
25 views
What is the critical string?
What is the critical string?
From wiki, I found the definition of non-Critical string
wiki
The non-critical string theory describes the relativistic string without enforcing the critical ...
4
votes
1answer
110 views
$SU(5)$ representation and higher anti-symmetric traces
In Zee QFT book v2 p.411 eq.16-17, he shows the SU(5) gauge theory anomaly cancellation by the following:
The 1st line in fundamental of SU(5)
$$
tr(T^3)=3(+2)^3+2(-3)^3=30,
$$
is easy to follow, ...
3
votes
0answers
98 views
Mathematics of Anomalies in QFT
As a mathematics student interested in theoretical physics, I found it very hard to study about anomalies in QFT in standard physics texts. They concentrate on particular examples (like chiral anomaly)...
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votes
2answers
597 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 ...
11
votes
1answer
196 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-...
5
votes
1answer
96 views
What happens to the $U(1)_B U(1)_Y^2$ anomaly in the Standard Model?
Baryon number $U(1)_B$ is anomalous in the Standard Model, as can be seen by computing a $U(1)_B SU(2)_L^2$ triangle diagram. This implies that
$$\partial_\mu J^{\mu B} \sim W_{\mu\nu} \tilde{W}^{\mu\...
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0answers
24 views
Gauging $U(1)_{B-L}$ in the absence of right-handed neutrinos
If we gauge the baryon minus lepton number symmetry $U(1)_{B-L}$, the mixed lepton-gravity-anomalies cancel in the presence of right-handed neutrinos (see e.g. this paper). However, if right-handed ...
3
votes
1answer
130 views
2D anomaly-free condition for a gauge theory
Take a $SU(2)$ gauge theory in 2d spacetime, say there are $n_1$ left-handed Weyl fermion in spin-1 written as
$$
1_L,
$$
and $n_0$ left-handed Weyl fermion in spin-0 written as
$$
0_L .
$$
and $n_{1/...
0
votes
1answer
72 views
Equality of positron and proton charge problem statement
When I hear that the equality of positron and proton charge is an unsolved problem I assume that we are putting the electric charge by hand in the electroweak section of the SM Lagrangian.
Is this ...
1
vote
0answers
60 views
$Z_1=Z_2$ without Ward-Takahashi identity?
In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...
2
votes
1answer
99 views
Simple explanation of the QCD VEV in terms of instantons
I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
2
votes
0answers
73 views
Feynman rules for anomalous vertex [closed]
We can read Feynman rules directly from the lagrangian in the simplest cases, but for the following lagrangian I am a few stuck
$\mathcal{L}=4g\phi\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}A_{\nu}\...
2
votes
0answers
80 views
Gauge anomaly from conformal dimension?
According to ref.1, the Chern-Simons theory $\mathrm{SU}(N)_k$ has a $\mathbb Z_N$ one-form symmetry with anomaly
$$
\eta=\exp\left[-2\pi i \frac{k}{N}\right]\tag{4.12}
$$
which, apparently, can be ...
0
votes
0answers
37 views
Dimensions and superstring theory [duplicate]
While I was reading B. Greene 's "the fabric of the cosmos" ,
There he says that the theory of relativity and quantum mechanics are the two pillars on which modern physics stands, but these theories ...
3
votes
1answer
117 views
Does the ABJ anomaly for the Abelian gauge field have a topological argument?
We known that the ABJ anomaly for non-abelian gauge fields with gauge group containing $SU(2)$ as a subgroup has a topological argument from the Euclidean path integral. Through studying the Euclidean ...
0
votes
1answer
52 views
Proposal of the Virasoro modes and algebra
Hi I am wondering what the first published paper on Virasoro modes was? And what about Virasoro algebra?
3
votes
0answers
101 views
Energy-Momentum Tensor and Variation of the Partition Function
I am currently working through the Fujikawa paper "Comments on Chiral and Conformal Anomalies". I have, however, had some issues getting around some notation, and perhaps a little of the logic, he ...
4
votes
1answer
138 views
Can a gauge anomaly be *removed* by quantum corrections?
Consider a classical gauge field coupled to a vector field $j^\mu$. Gauge invariance requires that $\mathcal A_\mathrm{cl}:=\partial_\mu j^\mu$ vanishes:
$$
\mathcal A_\mathrm{cl}\equiv 0
$$
In other ...
8
votes
0answers
127 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 ...
2
votes
0answers
254 views
Why does M-theory need 11 dimensions? [duplicate]
I have looked on the internet and no one can tell me why M-theory needs eleven dimensions?
2
votes
1answer
112 views
Parity Invariance of Path-Integral Measure
If a theory is parity invariant classically, is its path-integral measure also invariant under parity?
2
votes
1answer
101 views
axial anomaly for adjoint fermion v.s. fundamental fermion
It is known that the axial anomaly (chiral anomaly, the left L- right R) shows that $U(1)_A$-axial symmetry is not a global symmetry at quantum level.
In particular, one can consider the (1) ...
