All Questions
30
questions
1
vote
2
answers
108
views
Checks of anomaly cancellation
In a textbook I read that if $G$ is a global symmetry of the classical Lagrangian, then one has to check $G\times H^2$ anomalies, where $H$ is one of the SM gauge groups.
For example, when $G$ refers ...
- 51
0
votes
0
answers
69
views
Quantum (higher-form) anomaly at finite temperature
At finite temperature, anomaly is generally known to be contaminated, and thus the 't Hooft anomaly matching does not work after thermal compactification. Meanwhile, I have read paper saying that ...
- 81
1
vote
0
answers
61
views
Form of SM hypercharge current and anomalies
I have a doubt regarding the SM hypercharge current associated with the $U(1)_Y$ global symmetry (note: I want to work in the unbroken phase, we have the doublet H and the Yukawas)
$\psi \to e^{i\...
- 130
2
votes
0
answers
96
views
Vanishing Chern-Simons partition function
I was reading again the article "Generalized Global Symmetries" and I notice that in the beginning of page 22, they argue that after gauging the $\mathbb{Z}_k$ one-form symmetry, of Chern-...
- 451
14
votes
3
answers
3k
views
How are anomalies possible?
From Matthew D. Shwartz Quantum Field Theory textbook, he writes:
"Most of the time, a symmetry of a classical theory is also a symmetry of the quantum theory based on the same Lagrangian. When ...
- 2,599
3
votes
1
answer
327
views
How can Chiral symmetry protect the mass of a fermion if it's broken by quantization?
Suppose we have a Lagrangian invariant under Chiral symmetry, such as QED with massless fermions:
$$ \mathscr{L} = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \bar{\psi} i \gamma^{\mu} D_{\mu} \psi .$$
In ...
0
votes
2
answers
223
views
How can we show the Lorentz symmetry is not anomalous in $\phi^{4}$ theory?
how can I show in a lagrangian with scalar fields and $\phi^{4}$ interaction, the energy-momentum tensor isn't anomalous?
- 1
4
votes
1
answer
192
views
Anomalous global symmetry in non-gauge theories
I’m a bit confused on the effects of anomalous global symmetries. So take for instance the following theory
$$\mathscr{L}=\partial_\mu\phi\partial^\mu\phi^*+i\bar{\psi}\gamma_\mu\partial^\mu\psi-y \...
- 181
2
votes
0
answers
258
views
Confusion about chiral anomaly (Fujikawa's method)
I am reading Fujikawa's method for calculating chiral anomaly, see this wiki page.
The method can be described as follows.
It starts with the path integral
\begin{equation}
Z=\int\mathcal{D}\psi\...
- 995
5
votes
0
answers
171
views
Symmetries in quantum field theory and anomalies
Suppose we have a lagrangian quantum field theory, thus a theory where we can write an action in the form
\begin{equation}
S = \displaystyle \int d^4 x \; \mathcal L \, \left( \partial_{\mu} \phi , \...
- 141
2
votes
1
answer
302
views
Symmetry anomaly and energy spectrum
Let us consider 't Hooft anomaly:
\begin{eqnarray}
Z[A^\lambda]=Z[A]\exp(i\alpha[A,\lambda]),
\end{eqnarray}
where $A$ is the background $G$-gauge field and $\lambda$ is some $G$-gauge ...
- 813
10
votes
1
answer
754
views
Low energy description of Symmetry Enriched Topological phases
Prelude: low energy description of Symmetry Protected Topological (SPT) phases
It is known [1] that the low energy effective description of SPT phases, protected by a group $G$ is an invertible ...
- 4,654
3
votes
1
answer
130
views
If a regularization procedure respects a symmetry, is this symmetry unbroken in perturbation theory?
I read in this paper the statement that a proof that SUSY is preserved in perturbation theory would be the existence of a regularization procedure which respects SUSY (for a particular theory).
Is ...
- 1,982
5
votes
0
answers
109
views
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 ...
- 8,490
9
votes
1
answer
666
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[\...
- 26.8k