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.
1
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1answer
79 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
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0answers
99 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 ...
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0answers
29 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'...
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0answers
30 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
22 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 ...
3
votes
1answer
59 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
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0answers
67 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)...
10
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2answers
536 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 ...
6
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0answers
62 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
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1answer
60 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
$$\partial_\mu J^{\mu B} \sim W_{\mu\nu} \tilde{W}^{\mu\...
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0answers
22 views
Gauging $U(1)_{B-L}$ in the absence of right-handed neutrinos
If we gauge the baryon minus lepton number symmetry $U(1)_{B-L}$, the mixed lepton-gravity-anomalies cancel in the presence of right-handed neutrinos (see e.g. this paper). However, if right-handed ...
3
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1answer
104 views
2D anomaly-free condition for a gauge theory
Take a $SU(2)$ gauge theory in 2d spacetime, say there are $n_1$ left-handed Weyl fermion in spin-1 written as
$$
1_L,
$$
and $n_0$ left-handed Weyl fermion in spin-0 written as
$$
0_L .
$$
and $n_{1/...
0
votes
1answer
69 views
Equality of positron and proton charge problem statement
When I hear that the equality of positron and proton charge is an unsolved problem I assume that we are putting the electric charge by hand in the electroweak section of the SM Lagrangian.
Is this ...
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0answers
46 views
$Z_1=Z_2$ without Ward-Takahashi identity?
In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...
2
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1answer
73 views
Simple explanation of the QCD VEV in terms of instantons
I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
2
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0answers
42 views
Feynman rules for anomalous vertex [closed]
We can read Feynman rules directly from the lagrangian in the simplest cases, but for the following lagrangian I am a few stuck
$\mathcal{L}=4g\phi\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}A_{\nu}\...
2
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0answers
65 views
Gauge anomaly from conformal dimension?
According to ref.1, the Chern-Simons theory $\mathrm{SU}(N)_k$ has a $\mathbb Z_N$ one-form symmetry with anomaly
$$
\eta=\exp\left[-2\pi i \frac{k}{N}\right]\tag{4.12}
$$
which, apparently, can be ...
0
votes
0answers
30 views
Dimensions and superstring theory [duplicate]
While I was reading B. Greene 's "the fabric of the cosmos" ,
There he says that the theory of relativity and quantum mechanics are the two pillars on which modern physics stands, but these theories ...
3
votes
1answer
79 views
Does the ABJ anomaly for the Abelian gauge field have a topological argument?
We known that the ABJ anomaly for non-abelian gauge fields with gauge group containing $SU(2)$ as a subgroup has a topological argument from the Euclidean path integral. Through studying the Euclidean ...
0
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1answer
45 views
Proposal of the Virasoro modes and algebra
Hi I am wondering what the first published paper on Virasoro modes was? And what about Virasoro algebra?
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0answers
76 views
Energy-Momentum Tensor and Variation of the Partition Function
I am currently working through the Fujikawa paper "Comments on Chiral and Conformal Anomalies". I have, however, had some issues getting around some notation, and perhaps a little of the logic, he ...
4
votes
1answer
126 views
Can a gauge anomaly be *removed* by quantum corrections?
Consider a classical gauge field coupled to a vector field $j^\mu$. Gauge invariance requires that $\mathcal A_\mathrm{cl}:=\partial_\mu j^\mu$ vanishes:
$$
\mathcal A_\mathrm{cl}\equiv 0
$$
In other ...
8
votes
0answers
120 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
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0answers
130 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
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1answer
82 views
Parity Invariance of Path-Integral Measure
If a theory is parity invariant classically, is its path-integral measure also invariant under parity?
0
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0answers
26 views
Can quantum anomalous hall effect in ferromagnetic material be attribute to the internal B field?
I have learned that the berry flux in the brillouin zone is responsible for the intrinsic QAHE. But one of my professors explains the Quantum anomalous hall effect by arguing that the exchange ...
2
votes
1answer
66 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) ...
2
votes
1answer
167 views
Old-fashioned approach to neutral pion’s decay rate
I am uncomfy with the calculation of the neutral pion’s decay rate via the triangle anomaly diagram, which gets touted as evidence of three colors. The calculation invokes PCAC in the guise of the ...
2
votes
2answers
64 views
In what sense are quasiholes and quasiparticles “excitations” in Fractional Quantum Hall (FQH) systems?
In the theory of Fractional Quantum Hall states, one often sees quasi-holes and quasi-electrons (or quasi-particles) being called "excitations" from the ground state initially given by Laughlin (...
9
votes
1answer
190 views
How do anomalies work in the causal formulation of QFT?
In the Epstein-Glaser formulation of a QFT, the would-be divergences are taken care of by meticulously splitting the distributions that appear in the construction of the $S$-matrix (or correlation ...
2
votes
1answer
140 views
Why are critical dimensions and central charge linkable?
From wikipedia:
"In order for a string theory to be consistent, the worldsheet theory must be conformally invariant. The obstruction to conformal symmetry is known as the Weyl anomaly and is ...
5
votes
1answer
127 views
Anomalies and short-distance divergences$.$
Let $J$ be a certain Noether current
$$
J=J[\phi]
$$
where $\phi$ is a field. This object is classically conserved, although in the quantum-mechanical case it may be anomalous.
In the functional ...
6
votes
0answers
172 views
Anomalous Ward Identities and anomalous dimensions
Let us consider an action $S[\phi,\partial\phi]$ which is classically invariant under a transformation group $G$. The associated Noether current $\mathcal{J}^\mu$ is classically conserved, namely $\...
2
votes
1answer
149 views
Why must the conformal anomaly on string worldsheet be cancelled?
Viewing the coordinates of spacetime as fields on string worldsheet, the strings are described by the Polyakov action which presents conformal symmetry (including others) at the claasical level.
Now ...
3
votes
1answer
225 views
How to calculate an axial anomaly in 1+1 dimensions?
As far as I understand, an axial $U(1)$ transformation transforms a two-component spinor like
$$ \psi \to \psi'=\text e^{\text i\epsilon \gamma^5 }\psi,\qquad \psi=\begin{pmatrix}\psi_1\\\psi_2\end{...
2
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0answers
66 views
Anomalous triangle vertex: divergencies and symmetry argument
Consider triangle correlator of one axial-vector current $J_{\lambda 5}$ and two vector currents $J_{\mu}, J_{\nu}$ in a theory with a fermion with mass $m$:
$$
\Gamma_{\lambda \mu\nu}(q,p,k) = F\bigg[...
3
votes
1answer
89 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. ...
1
vote
2answers
155 views
Conformal theory with zero central charge
Suppose there is a conformal field theory which has the global conformal symmetry namely $SL(2,R).$ and after central extension it is enhanced to Virasoro algebra with central charge, $c=0$ (also ...
5
votes
1answer
152 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 ...
12
votes
3answers
640 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 ...
0
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0answers
61 views
What is so complex in Hall effect?
I read that Zohar Ringel and Dmitry Kovrizhi of the University of Oxford have proven that creating a computer simulation of one of Earth's phenomena is currently impossible. Technology is not able to ...
0
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0answers
72 views
Can the 't Hooft anomaly of continuous symmetry restrict the spectrum to be gapless?
Let us consider a gapless system $X$ with a global continuous symmetry $G$ only, and no discrete symmetry. In addition, this system has $G$-'t Hooft anomaly, namely that $X/G$ is anomalous.
I wonder ...
1
vote
1answer
112 views
How to derive an $E_8$ algebra?
What is the simplest way to derive an $E_8$ algebra? I am not interested in $E_8$ itself but what would compel one to think about it. I know for example why you would want to think about $SU(2)$ and ...
5
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1answer
110 views
Are anomalies a failure of the canonical quantization prescription? Why not?
I would like to understand anomalies from the point of view of the canonical quantization. Noether's theorem claims that, given a continuous symmetry of the Lagrangian, there exists a function Q in ...
1
vote
1answer
74 views
Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit?
Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit?
From undergraduate quantum mechanics, I know that we ...
2
votes
1answer
156 views
Is it the chiral anomaly which is solely responsible for having instanton effects (and therefore, the $\theta-$term) in the QCD action?
$\textbf{Fact 1}$ In principle, the QCD Lagrangian should contain a Lorentz invariant, gauge invariant, dimension-4 term $\sim\theta \text{Tr}[F^{\mu\nu}\tilde{F}_{\mu\nu}]$. This term, however, is ...
4
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1answer
129 views
Anomalies of QCD
I have come across the following statement:
The anomalies of QCD cannot be reproduced by a collection of free fermions
carrying $U(1)_V$, $SU(N_f)_L$ and $SU(N_f)_R$ quantum numbers. That is why ...
15
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0answers
200 views
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 ...
3
votes
1answer
257 views
Axial anomaly in QCD VS axial anomaly in current algebra QCD
I would like to understand the distinction between an axial anomaly in QCD (Theta Vacuum: axion -> 2 gluons) and an axial anomaly in QCD of current (Chern–Simons term: pion->two photons, photon->three ...
2
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1answer
138 views
Possible typo in Schwartz's QFT, p. 629
I'm trying to see whether this is my own misunderstanding or a typo in Schwartz's QFT book. Any help or feedback appreciated.
Schwartz talks about Chiral anomalies from the integral measure. The ...
