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.
294
questions
2
votes
0answers
26 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 (23.6.6) appears to ...
1
vote
1answer
63 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
votes
0answers
88 views
What intuition led to J. Wang and X.G. Wen's lattice formulation of the 3450 chiral gauge theory?
In the paper cited below, Juven Wang and Xiao-Gang Wen give an example of a lattice model that reduces to a chiral $U(1)$ gauge theory at low energy. The low energy theory is called the $3450$ model. ...
6
votes
0answers
231 views
Holomorphic instantons in target torus
For computing instantons contributions from worldsheet torus to target torus, one can evaluate zero modes contribution of genus 1 partition function given by following expression:
$$Tr(-1)^FF_LF_Rq^{...
4
votes
2answers
170 views
Inconsistency in the normal ordered Virasoro algebra
I seem to have found a basic contradiction when it comes to the commutation relations of the Virasoro algebra with normal ordered operators and I am not sure what the resolution is.
If we have a ...
5
votes
1answer
143 views
Holomorphic anomaly at genus 1
Partition function on torus can be defined using a generalized Witten like index as given below:
$$F_1=\int_\mathbb{T}\frac{d^2\tau}{\tau_2} Tr(-1)^F F_LF_R \;q^{L_0} \bar{q}^{\bar{L_0}},$$
where $\...
2
votes
1answer
57 views
Chiral vortical effect (CVE) and gravitational anomaly
Chiral vortical effect is a generation of an axial current in the presence of the rotation.
On the one hand, the expression for the $\mathbf{CVE}$ has the following form:
$$
\vec{J}^{5} = \vec \Omega \...
3
votes
0answers
48 views
Anomalies in the self-dual Yang-Mills theory and $\mathcal{N}=2$ open-string theory
I am reading a paper, written by G. Chalmers and W. Siegel - https://arxiv.org/abs/hep-th/9606061, where they discuss the action of self-dual Yang-Mills theory, which in light-cone formalism is ...
3
votes
1answer
54 views
Regularization of $\delta$ function and Chiral anomaly in gravity
Mark Srednicki's QFT book presents a regularization of the $\delta$ function in calculating the chiral anomaly (see section 77 of the book). This regularization reads
\begin{equation}
\delta (x-y)=\...
0
votes
1answer
43 views
Why color anomaly is in the axion photon coupling?
The axion photon coupling is given by the expression
$ g_{a\gamma\gamma}= \frac{\alpha}{2\pi f_a}(\frac{E}{N}-\frac{2}{3}\frac{4m_d+m_u}{m_d+m_u}) $, where $f_a$ PQ symmetry breaking scale, $E$ and $...
3
votes
1answer
67 views
Anomalous global symmetry in non-gauge theories
Iām a bit confused on the effects of anomalous global symmetries. So take for instance the following theory
$$\mathscr{L}=\partial_\mu\phi\partial^\mu\phi^*+i\bar{\psi}\gamma_\mu\partial^\mu\psi-y \...
2
votes
0answers
69 views
Confusion about chiral anomaly (Fujikawa's method)
I am reading Fujikawa's method for calculating chiral anomaly, see this wiki page.
The method can be described as follows.
It starts with the path integral
\begin{equation}
Z=\int\mathcal{D}\psi\...
3
votes
1answer
83 views
How do we know there doesn't exist an anomaly that implies that there is no good choice of dimension for the bosonic string?
By considering $\langle T^\alpha_\alpha\rangle$, the Weyl anomaly, we can show that the critical dimension, $D=26$ is the only possible choice of dimension for the bosonic string.
However, how do we ...
9
votes
0answers
117 views
Does the Gibbons-Hawking boundary action have an anomaly inflow interpretation?
The Einstein-Hilbert action on a manifold $M$ with boundary is
$$\frac{-1}{16\pi G}\int_M d^n x \sqrt{-g} R +\frac{1}{8\pi G} \int_{\partial M} d^{n-1}x \sqrt{|h|} K$$
where $K$ is the extrinsic ...
6
votes
1answer
103 views
On-site symmetries can be gauged, but is a gaugeable symmetry necessarily on-site?
I've always liked lattice QFT because it's mathematically unambiguous and non-perturbative, but it does have two drawbacks: (1) the lattice is artificial, and (2) some features are messy. One of those ...
4
votes
1answer
151 views
How can we know a gauge theory is not anomalous?
Say we have a putative 4d gauge theory coupled to fermions of various representations. In order for this theory to be consistent, we need to check that no there are both no triangle anomalies and no ...
3
votes
0answers
139 views
Weyl Anomaly Derivation in Polchinski Eq (3.4.21)
In Polchinski's longer derivation of the Weyl anomaly, he arrives at the result (equation 3.4.19):
$$ \ln{\frac{Z[g]}{Z[\delta]}} = \frac{a_1}{8\pi} \int d^2\sigma \int d^2\sigma' g^{1/2} R(\sigma) G(\...
4
votes
1answer
71 views
Bosonic SPT phases with time reversal and a $Z_2$ symmetry
Consider a bosonic system with time reversal symmetry $\mathcal{T}$ and a unitary on-site $\mathbb{Z}_2$ symmetry. Suppose the symmetry is realized in a special way such that $$\mathcal{T}^2= (-1)^B$$ ...
1
vote
0answers
30 views
Conformal and chiral anomalies
In presentation On conformal anomalies
of some 6d superconformal theories was mentioned that there are some relations between chiral/gravitational and conformal anomalies.
For me, it is very ...
4
votes
1answer
110 views
Phenomenology application of quantum anomaly
Anomaly means that: the system has a symmetry at classical level (both discrete and continous), but when we quantize the theory, the system no longer holds the symmetry.
I'm wondering for every ...
4
votes
0answers
63 views
How does anomaly inflow work in terms of the eta invariant?
I'm trying to understand the non-perturbative picture of anomaly inflow, mainly following these two articles by Witten and Yonekura:
[1] - https://arxiv.org/pdf/1909.08775.pdf ,
[2] - https://arxiv....
4
votes
0answers
101 views
't Hooft anomaly implies spontaneous symmetry breaking?
It isn't clear to me why an 't Hooft anomaly implies spontaneous symmetry breaking. I would like to see an argument which shows this.
The most I can say about this scenario is that if the symmetry ...
3
votes
0answers
69 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 , \...
2
votes
1answer
97 views
Calculating traces for triangle diagrams with massless fermions
I am following Schwarz Quantum Field Theory textbook. In particular, I am looking at triangle diagrams with massless fermions. On pg. 623 - 624 Schwarz attempts to calculate $q_\mu^1 M_{5}^{\alpha\mu\...
1
vote
1answer
70 views
Axial anomaly at the level of particles
Consider pure QED with massless electrons. Due to the axial anomaly the axial current is not conserved:
$$
\tag 1 \partial_{\mu}J^{\mu}_{5} \sim F_{\mu\nu}\tilde{F}^{\mu\nu}
$$
On the other hand, it ...
2
votes
1answer
80 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 ...
0
votes
1answer
50 views
Fujikawa Jacobian for Baryon number anomaly
Reviewing the anomalies of the standard model, one knows that the Baryon number is not conserved because of an anomaly associated to the global $U(1)$ symmetry that quarks have. That is the current
$$...
1
vote
1answer
78 views
What's the difference and connection between symmetry breaking and anomaly?
I'm just wondering what's the difference between symmetry breaking and anomaly.
From my understanding, symmetry breaking means: there is a symmetry in the action, but in the ground state of the ...
2
votes
0answers
43 views
Chiral anomaly in Weyl semimental
In Weyl semimetal, there is an analog of ABJ anomaly, which is a $E \cdot B$ term. The ABJ anomaly can be viewed as winding number because of the homotopy group of sphere $\pi_3(S^3)= \mathbb{Z}$ for ...
0
votes
0answers
51 views
Chiral anomaly for massless Dirac fermion
Let us assume we have a single flavor massless Dirac fermion with Lagrangian $\mathcal{L} = \bar{\psi}i\gamma^{\mu}D_{\mu}\psi + \mathcal{L}_{gauge}.~$ Due to chiral anomaly, chiral symmetry is not a ...
1
vote
0answers
58 views
Gauge invariance of the regulator when calculating the chiral (ABJ) anomaly by the Fujikawa method
I am currently studying the calculation of chiral anomaly using fermionic path integral.
In all texts I looked at, the authors simply use a regulator of the following form $e^{(\gamma_{\mu}D^{\mu})^...
7
votes
1answer
273 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 ...
8
votes
1answer
128 views
Among free quantum field theories, do all 't Hooft anomalies arise from chiral fermions?
In quantum field theory, a global symmetry group that can't be gauged is said to have an 't Hooft anomaly. One of the most familiar examples is the free massless Dirac fermion in $3+1$ dimensional ...
6
votes
1answer
119 views
Can Lorentz/Poincare symmetry be anomalous?
The question is in the title. Can a Poincare invariant Lagrangian lead to a path integral that is not Lorentz or Poincare invariant? If so, can I have an example?
A related confusion: on page 426 of ...
11
votes
1answer
214 views
Why do we solve the Wess-Zumino consistency condition using the method of descent?
Consider a quantum field theory in $d$ dimensions with a symmetry $G$. For the purpose of this discussion let's say that $d$ is even and $G$ is a compact, connected Lie group. We say that the symmetry ...
3
votes
2answers
126 views
Are there versions of String Theory formulated in $D$ spacetime dimensions or even in infinitely many dimensions?
There are a lot of different versions of string theory, and almost all of them differ in the number of dimensions. The most famous ones are formulated in 10, 11 or 26 dimensions.
But are there any ...
8
votes
1answer
281 views
't Hooft vs ABJ anomalies [closed]
At some point in our physics education, we begin to accumulate a bunch of slogans related to anomalies. At some (later, in my case) point, we learn that actually there were two different kinds of ...
2
votes
0answers
110 views
Integral in direct calculation of anomalies
I am trying to follow Weinberg's triangle diagram calculations in section 22.3 of volume II of The Quantum Theory of Fields. He reduces the calculation to evaluating the integral
\begin{equation}
\...
2
votes
1answer
115 views
Chiral anomaly: UV or IR effect
In TASI 2003 Lectures on Anomalies (section 1.6) Jeffrey A. Harvey present arguments, why chiral anomaly is IR effect (in contrast to calculation, where UV regulator was used):
Only massless ...
5
votes
2answers
313 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, ...
2
votes
1answer
116 views
Anomalies on boundary and bulk physics
Few times I faced with such statements:
The gravitational anomaly of the 1+1d boundary system is known to be
proportional to the thermal Hall conductivity of the 2+1 dimensional
bulk
How ...
8
votes
0answers
201 views
't Hooft Anomaly Equivalent Definitions
I've seen a 't Hooft anomaly defined in two ways. Roughly, a theory has a 't Hooft anomaly when
Once the theory is coupled to a background gauge field $A$ (so study eg the partition function $Z[A]$), ...
2
votes
0answers
129 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}\...
6
votes
0answers
206 views
Classification of higher Symmetry Protected Topological (SPT) phases
Suppose that we have a $d$ dimensional bosonic SPT phase, protected by some $p$-form symmetry, $G^{[p]}$. Suppose also that it is classified within group cohomology, so that we don't have to run into ...
4
votes
1answer
135 views
Loop counting for determinants and anomalies
I am trying to understand an argument for why anomalies are one-loop exact, given by Bilal in Lectures on Anomalies. The relevant paragraph is reproduced here:
Let us first explain why the anomaly ...
1
vote
0answers
52 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; $...
2
votes
1answer
90 views
Chiral anomalies and triangle diagrams
In the computation of the Adam-Bell-Jackiw anomaly, in Peskin and Schroeder's book they proceed with a regularization of $\partial_\mu j^{\mu 5}$ by evaluating the fields at different spacetime points ...
5
votes
2answers
691 views
Anomalies in QFT
I am a first year PhD student in theoretical physics with a background in QFT (up until relativistic fields, path integrals and gauge theories and anomalies) and some algebraic topology but my ...
7
votes
1answer
150 views
Why do we think that the $U(1)$ problem is solved by instantons?
It is usually thought that the $U(1)$ problem is solved when 't Hooft realized that instantons induce additional symmetry breaking of the $U(1)_A$ symmetry aside from the non-vanishing quark masses. ...
1
vote
0answers
42 views
Gravitational correction in index theorem for 3+1 time-reversal invariant TI
In Witten's review paper: Fermion path integrals and topological phases, the index theorem for 3+1 $\mathcal{T}$-conserving TI is given by
$$e^{\mp i\pi \eta/2}e^{\pm i\pi(P-\hat{A}(R))}=(-1)^{\...
