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.
2
votes
1answer
42 views
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)}\...
4
votes
0answers
35 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 ...
6
votes
2answers
78 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:
$$
\mathcal L=\frac12m\dot q^2-\frac{i}{...
4
votes
1answer
81 views
Why does a triangle anomaly appear in a gauge theory?
I have read that when we construct a theory with abelian gauge symmetry there will appear some anomalies when we do the quantum correction to the theory. In 4D space such anomalies are explained by ...
1
vote
0answers
63 views
Higher point anomalies cancellation from trace
I had asked this question within this one before, but having also made other 2 independent enough questions there, decided to ask this one by itself here.
So, it is a well known fact that the ...
0
votes
1answer
52 views
Nuclei violating B number
Within SM, it is know that baryon number is not preserved and changes as
$$
\Delta B = 3·\Delta n_{CS}, \quad n_{CS} \in \mathbb{Z}\ ({\rm Chern-Simons\ index\ for\ vacuum})
\tag1$$
Then, its ...
0
votes
0answers
37 views
B violation and electric charge
Within SM you can prove that despite we have baryon number conservation respect to Noether theorem, at quantum level baryon (and lepton) number is violated as
$$
\Delta B = 3·\Delta n_{CS}, \quad n_{...
1
vote
0answers
97 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. ...
1
vote
0answers
27 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
1answer
49 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{...
9
votes
3answers
295 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 ...
6
votes
0answers
210 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 ...
0
votes
0answers
74 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):
$$
\...
0
votes
0answers
31 views
References to understand BRST Quantization
I'm looking for good, rigorous references that discuss BRST quantization in relation to how it leads to dealing with anomalies and ghost fields. I'm looking at high level references (i.e., assume ...
0
votes
0answers
35 views
QCD Trace Anomaly and Mass
In the paper in equations 4 and 5, some of the mass of the nucleons comes from the "trace anomaly" of the QCD energy-momentum tensor (as described in the paragraph following these equations). Is there ...
5
votes
2answers
259 views
How do anomalies affect the field equations of motion?
I find anomalies an extremely unintuitive subject, because they're studied so indirectly. In the standard textbook presentation, one computes an abstract quantity that should be zero classically (say, ...
2
votes
0answers
42 views
How does the Weyl anomaly imply $\langle T^{\mu}_{\mu} \rangle \neq 0$
I want to consider the case of euclidean field theory in 2 dimensions with the action
$$S[\phi]=\int \! d^2\!x \sqrt{\det(g)}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$$
which leads to a partition ...
3
votes
1answer
85 views
Does the massless fermion in $2+1$ dimensions suffer from gauge anomaly?
In Fermion Path Integrals And Topological Phases Witten showed that for a massless Dirac fermion in $2+1$ dimensions
$$S[\bar{\psi},\psi]=\int d^{3}x\bar{\psi}iD\!\!\!\!/_{A}\psi,$$
where $A$ is a $...
2
votes
1answer
94 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
76 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
44 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
296 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
159 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
93 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
211 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 ...
1
vote
0answers
119 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
194 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
159 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
59 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
102 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.
...
3
votes
1answer
109 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\...
4
votes
1answer
162 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
113 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
136 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
40 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
43 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 $\...
0
votes
0answers
26 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
137 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
110 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)...
11
votes
2answers
610 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 ...
10
votes
1answer
208 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-...
4
votes
1answer
101 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
$$\partial_\mu J^{\mu B} \sim W_{\mu\nu} \tilde{W}^{\mu\...
0
votes
0answers
27 views
Gauging $U(1)_{B-L}$ in the absence of right-handed neutrinos
If we gauge the baryon minus lepton number symmetry $U(1)_{B-L}$, the mixed lepton-gravity-anomalies cancel in the presence of right-handed neutrinos (see e.g. this paper). However, if right-handed ...
3
votes
1answer
135 views
2D anomaly-free condition for a gauge theory
Take a $SU(2)$ gauge theory in 2d spacetime, say there are $n_1$ left-handed Weyl fermion in spin-1 written as
$$
1_L,
$$
and $n_0$ left-handed Weyl fermion in spin-0 written as
$$
0_L .
$$
and $n_{1/...
0
votes
1answer
73 views
Equality of positron and proton charge problem statement
When I hear that the equality of positron and proton charge is an unsolved problem I assume that we are putting the electric charge by hand in the electroweak section of the SM Lagrangian.
Is this ...
1
vote
0answers
67 views
$Z_1=Z_2$ without Ward-Takahashi identity?
In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...
2
votes
1answer
109 views
Simple explanation of the QCD VEV in terms of instantons
I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
2
votes
0answers
85 views
Feynman rules for anomalous vertex [closed]
We can read Feynman rules directly from the lagrangian in the simplest cases, but for the following lagrangian I am a few stuck
$\mathcal{L}=4g\phi\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}A_{\nu}\...
2
votes
0answers
81 views
Gauge anomaly from conformal dimension?
According to ref.1, the Chern-Simons theory $\mathrm{SU}(N)_k$ has a $\mathbb Z_N$ one-form symmetry with anomaly
$$
\eta=\exp\left[-2\pi i \frac{k}{N}\right]\tag{4.12}
$$
which, apparently, can be ...
3
votes
1answer
128 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 ...
