All Questions
Tagged with anomaly or quantum-anomalies
82 questions
7
votes
2
answers
2k
views
Anomaly inflow mechanism
I know very simple example of anomaly inflow. See section 4.4 in David Tong: Lectures on Gauge Theory. As I read, such mechanism have some applications in condensed matter and in quantum field theory, ...
- 5,737
7
votes
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
6
votes
1
answer
2k
views
Chiral anomaly in Weyl semimetal
In the presence of electromagnetic fields $E$ and $B$, four current is not conserved in a Weyl semimetal i.e. $\partial_{\mu} j^{\mu}\propto E\cdot B \neq 0$. There are some proofs in the literature ...
- 135
6
votes
1
answer
2k
views
Virasoro Algebra vs Witt Algebra
I'm reading some notes on CFT, and there's a strange topic that I find quite confusing. We define the Witt algebra to be the generators of conformal transformations on the complex plane.
$l_n = -z^{...
- 295
5
votes
1
answer
721
views
Anomaly cancellation and fermion number violation
In the standard model, an axial $SU(3)$ currents has anomaly which after quantization leads to the fermion number violation. However, taking all the fermions into account we note that the anomalies ...
- 114
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
5
votes
2
answers
585
views
Kaluza-Klein in superstring theory
In superstring theory, it says that they wrap 16 dimensions on a torus given by $\mathbb{R}^{16}$ divided by a SO(32) or $E_8 \times E_8$ lattice and this gives a gauge group of the same name.
But in ...
user84158
5
votes
1
answer
1k
views
Ambiguity in Beta Functions (2-loop)
Beyond one-loop, the beta function of a QFT is scheme dependent. I would like to understand better this ambiguity.
The easiest thing to say is that you haven't calculated something physical, so of ...
- 2,707
5
votes
1
answer
490
views
Definition of anomalous symmetry in Hamiltonian formalism
In the Lagrangian path-integral formulation of QFT, an anomalous symmetry is defined to be a symmetry of the action which is not a symmetry of the measure of the path integral, and therefore not a ...
- 49.4k
5
votes
1
answer
646
views
Is this explanation of "Why nine space dimensions?" correct?
In Gordon Kane's Supersymmetry and Beyond (p. 118), he states:
String theory has to be formulated in nine space dimensions or it is not a consistent mathematical theory. There doesn't seem to be a ...
- 6,817
4
votes
1
answer
373
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
$$
\sum_{k=1}^\ell\...
4
votes
1
answer
980
views
Axial anomaly in QCD VS axial anomaly in current algebra QCD
I would like to understand the distinction between an axial anomaly in QCD (Theta Vacuum: axion -> 2 gluons) and an axial anomaly in QCD of current (Chern–Simons term: pion->two photons, photon->three ...
- 215
3
votes
1
answer
983
views
Gauge anomalies ruin the unitarity - the explanation involving ghosts
An outline
As is known, the presence of gauge anomalies leads to breakdown of the unitarity of the gauge theory.
One way to understand this is to involve the BRST quantization of the gauge field ...
- 8,971
3
votes
1
answer
174
views
$U(1)_A$ effects on the baryons?
We know that the axial $U(1)_A$ is anomalous thus not a global symmetry. Therefore there is no direct associated pseudo goldstone boson for $U(1)_A$. This makes the $\eta'$ much more massive than the ...
- 4,376
3
votes
0
answers
92
views
The sign of axion $F$ $F$ dual term in Weinberg
Related to the earlier question $\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki.
The sign of axion $F$ $F$ dual term in Weinberg (23.6.16) appears to ...
- 4,376
3
votes
0
answers
344
views
Polchinski Weyl Anomaly from perturbing the flat background. Eq (3.4.22)
In deriving the Weyl anomaly for the bosonic string using a perturbation around a flat background, Polchinksi uses Eq. (3.4.22), i.e.
$$
\ln \frac{ Z[\delta+h] }{Z[\delta]} \approx\, \frac{1}{8\pi^2}\...
- 3,165
3
votes
1
answer
493
views
Significance of total divergence anomaly term
What is the significance of the fact that the anomany term (calculated from the triangle diagram) is a total divergence? Or, in other words, what is the significance of $$\partial_\mu j^\mu_A\sim Tr(W\...
- 27.2k
3
votes
1
answer
776
views
Is it the chiral anomaly which is solely responsible for having instanton effects (and therefore, the $\theta-$term) in the QCD action?
$\textbf{Fact 1}$ In principle, the QCD Lagrangian should contain a Lorentz invariant, gauge invariant, dimension-4 term $\sim\theta \text{Tr}[F^{\mu\nu}\tilde{F}_{\mu\nu}]$. This term, however, is ...
- 27.2k
3
votes
0
answers
288
views
Hamiltonian Operator Interpretation of Quantum Anomaly
We can see the definition of quantum anomaly in terms of Lagrangian path integral formulation. What is the definition of quantum anomaly in terms of Hamiltonian operator approach or even more directly ...
- 749
3
votes
1
answer
1k
views
The non-abelian chiral anomaly and one-loop diagrams higher than the triangle one
Suppose chiral fermions $\psi$ interacting with gauge fields $A_{\mu,L/R}$. With $P_{L/R} \equiv \frac{1\mp\gamma_{5}}{2}$ and $t_{a,L/R}$ denoting the generators, the corresponding action reads
$$
S =...
- 8,971
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
2
votes
1
answer
309
views
$\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki
The theta angle due to the chiral gamma^5 rotation of chiral fermion results in the phase alpha(x) that has different + or - sign for
(1) Peskin&Schroeder, (2) Weinberg or (3) Srednicki.
Here
...
- 4,376
2
votes
1
answer
277
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) ...
- 4,376
2
votes
1
answer
891
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 ...
- 3,137
2
votes
1
answer
735
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 ...
- 3,741
2
votes
0
answers
391
views
Cutkosky rule for the triangle diagram
Outline - the anomalous vacuum polarization correction
Suppose the abelian anomalous gauge theory (with axial gauge field $A$, vector gauge field $V$ and single massless fermion $\psi$):
$$
\tag 1 L =...
- 8,971
2
votes
1
answer
719
views
Consequences of local and global anomaly
Are the physical consequences of anomalies associated with a local symmetry is different from that of a global symmetry? If yes, why? We have global anomaly in the standard model but not local anomaly?...
- 27.2k
2
votes
2
answers
393
views
Can we allowe gauge non-invariant terms in a gauge theory?
In a gauge theory, the tree-level Lagrangian is gauge invariant. Is it possible that a gauge non-invariant term induced in the Lagrangian via loop-effects (may be by integrating out certain fields)?
- 27.2k
1
vote
0
answers
223
views
The anomalous Hall effect in Weyl semimetals
Suppose the semimetal - the solid material, in which the conducting and valence zones are intersected at isolated points - the so-called Weyl nodes. Near this points, the Hamiltonian of electrons is ...
- 8,971
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
1
vote
0
answers
273
views
Why the contact terms in the Ward identity vanish due to the invariant Noether currents?
The picture below is a screenshot of Srednicki's QFT textbook.
------------------------------
------------------------------
$j^{\mu}$ is the current associated with the $U(1)$ gauge symmetry; $...
- 109
0
votes
0
answers
320
views
Anomalous commutators and gauge anomaly
Suppose we know, that the dynamics of theory with chiral fermions (say, left) and gauge field (for simplicity, abelian) leads us to presence of anomalous commutator of canonical momentum $\mathbf E(\...
- 8,971