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.
390
questions
1
vote
1
answer
27
views
About the anomaly of $R$-symmetry
We know that in 4d $\mathcal{N}=1$, we usually determine the real $R$-symmetry by declaring that it is not anomalous. However, in 2d $\mathcal{N}=(2,2)$, there is a genuine anomaly of $U(1)$ $R$-...
- 49
3
votes
1
answer
63
views
How to confirm that a QFT is a conformal field theory (CFT) at the quantum level?
My question is: Given a QFT, what's the usual/reliable/logical way to confirm that it's a CFT at the quantum level? Here are some explanations about why I ask this question.
I have learned a lot about ...
- 329
4
votes
0
answers
50
views
Gauge Anomalies General scenario using Fujikawa Method
I would like to ask a question about Gauge Anomalies and how we can extract them through the Fujikawa method, without using the general triangle diagram as proposed by Weinberg Volume 2 Chapter 22.3.
...
- 71
1
vote
2
answers
125
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
66
views
Simplified Explanation of Coleman-Weinberg Potential in QFT
I have been reading a research paper where the interaction potential between two scalar fields is given by $$=g\, \phi H^\dagger H .$$ The Coleman-Weinberg correction to the potential is: $$ \frac{n}{...
- 117
2
votes
0
answers
69
views
Konishi operator anomalous dimension [closed]
The Konishi operators are operators in the ${\cal N}=4$ SYM theory and are given by:
$$ K = \sum _{i=1}^6Tr\ (\phi^i\phi^i) $$
The 2 point function of this operator is:
$$ \big\langle K(x)K(y)\big\...
- 411
3
votes
0
answers
84
views
Application of Callias operator in physics
In his article "Axial Anomalies and Index Theorems on Open Spaces" C.Callias shows how the index of the Callias-type operator on $R^{n}$ can be used to study properties of fermions in the ...
- 31
12
votes
1
answer
144
views
Is there a conceptual inverse of anomalies i.e. a notion of quantum enhancement of symmetries?
Anomalies usually occur when a classical symmetry ceases to be a symmetry of the theory when quantized. Are there quantum systems with certain symmetries which cease to exist when you take classical ...
- 803
1
vote
0
answers
47
views
Regarding vanishing of a triangle diagram
Furry's theorem ($C$ symmetry) is very important in calculations in QCD, Electroweak theory. Primarily it says everything about QED (three photon triangle diagram), but can be extended to QCD, and ($Z$...
- 554
0
votes
0
answers
50
views
How many dimensions are in string theory? [duplicate]
How many dimensions are in string theroy? I heard that there are 11 but to my understanding, there is an infinite, also can strings be on a 2D plane?
2
votes
1
answer
125
views
Topological behavior (or asymptotics at infinity) of gauge fields assumed in Fujikawa method
Chiral anomaly is computed very elegantly by Fujikawa method, which is also presented in Section 22.2 of Weinberg QFT textbook volume 2 or wikipedia.
Here, the underlying spacetime is assumed to be $\...
- 1,669
2
votes
1
answer
80
views
Why the expectation value of three currents is important in the anomaly?
I am studying the anomalies chapter (Chapter 30) of Schwartz's [Quantum Field Theory and the Standard Model]. I want to ask why the expectation of three currents, $\langle J^\mu J^\nu J^\rho \rangle$, ...
- 79
1
vote
0
answers
66
views
Reference request scale anomaly
Can anyone recommend some books, notes and review-oriented papers on scale anomaly, with a view towards its relation to renormalization? Such as an anomaly perspective on RG, Callan-Symanzik equations ...
1
vote
0
answers
35
views
Axion domain wall number and heavy quarks
The domain wall number of a UV complete theory of axion is related to the number of PQ-charged heavy quarks that run in the loop. In the case of KSVZ model, $N_{\rm DW}=1$ while in DFSZ, $N_{\rm DW}&...
- 61
3
votes
0
answers
102
views
Relation between the Casimir energy and the central charge in CFT in general
In 2d CFT we know that the Casimir energy of the vacuum is proportional to the conformal central charge $c$.
$$
F_L=f_0 L-\frac{\pi c}{6 L} \tag{1}
$$
where $F$ is the free energy and L is the ...
- 31
0
votes
0
answers
28
views
What is the correct type of the Berry curvature?
I am studying Berry curvature for a specific material and faced different types of the Berry curvature formula. Some papers use only valence eigenstates (u1) like this $$i*(<(∂U1/∂kx)| (∂U1/∂ky)>...
0
votes
0
answers
78
views
Point-splitting regularization for anomaly in curved spacetime
In flat spacetime, the point-splitting regularization for (chiral) anomaly is discussed in great details in Peskin and Schroeder's QFT.
Does anyone know any good references for calculating anomaly ...
1
vote
0
answers
39
views
Axial anomaly for odd dimension
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
- 71
2
votes
0
answers
107
views
Axial Chiral Anomaly
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
- 71
1
vote
1
answer
89
views
Non-Abelian anomaly: why does non-Hermitian operator have complete basis of eigenvectors?
In section 13.3 of his book [1], Nakahara computes the non-Abelian anomaly for a chiral Weyl fermion coupled to a gauge field by making use of an operator
$$
\mathrm{i}\hat{D} = \mathrm{i}\gamma^\mu (\...
- 2,157
3
votes
0
answers
84
views
Questions about the treatment of anomalies
I was reading Schwartz's QFT book, and in Chapter 30, he introduces the calculations of anomalies by evaluating objects like $\partial_\mu\langle J^{\mu 5}J^\nu J^\alpha\rangle$, where $J^5$ is ...
- 348
0
votes
1
answer
137
views
Peskin and Schroeder Chapter 19 anomalies 19.63 Lagrangian
I am (self) studying chapter 19 of Peskin and Schroeder's Introduction to Quantum Field Theory. Around equation (19.63) they state the Lagrangian is invariant if $\alpha$ is a constant, and if $\...
- 57
3
votes
1
answer
131
views
How is the dimensionful renornalization scale $\mu$ related to break of scale invariance in String Theory?
In the $7.1.1$ of David Tong's String Theory notes it is said the following about regularization of Polyakov action in a curved target manifold:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
- 1,300
2
votes
1
answer
128
views
Why does fermion have the expansion with Grassmann-numbers?
I learn the chiral anomaly by Fujikawa method. The text book "Path Integrals and Quantum Anomalies, Kazuo Fujikawa", in the page 151, says that
…one can define a complete orthonormal set $\{...
- 129
1
vote
0
answers
60
views
Unitarity of Effective String Theory away from critical dimesions ($D=26$) , in the static gauge
Starting from compete UV description of QCD (in the confined phase), if we integrate out the quarks and Glueballs, in principle, we will get an effective theory of strings (QCD flux tube and not ...
- 11
1
vote
0
answers
133
views
Trying to derive chiral anomaly in 2D from Feynman diagrams in position space
Trying to understand the Chiral anomaly, I decided to explore the simplest example of a holomorphic fermion in 2D in a background electromagnetic field $A\text{d}z+\bar{A}\text{d}\bar{z}$. The ...
- 3,925
1
vote
0
answers
42
views
Is there a "unification" explanation of why the mixed gauge-gravitational anomaly cancels in the standard model?
Quoting the Review of Particle Physics (93.2.3):
all representations of SO(10) are anomaly free in four dimensions... the absence of anomalies in ... a SM generation can be viewed as deriving from ...
- 13.1k
1
vote
1
answer
203
views
Getting rid of the theta term in the standard electroweak theory
This has already been asked here more than once, but the existing answers do not tackle my misunderstanding.
A topological $\theta$-term is understood to be physical, in the usual particle model ...
- 1,752
9
votes
2
answers
841
views
How is the pion related to spontaneous symmetry breaking in QCD?
In chapter 19 of An Introduction to Quantum Field Theory by Peskin & Schroeder, they discuss spontaneous symmetry breaking (SSB) at low energies in massless (or nearly massless) QCD, given by
$$\...
- 101
2
votes
0
answers
74
views
Goldstone bosons in 2 and 3 quark flavor symmetries [closed]
In my (undergraduate) advanced elementary particles class last semester, we learnt that for a 2 quark (u/d) model the symmetry of the Lagrangian is (and breaks as)
$$
U(2)_L \otimes U(2)_R = SU(2)_L \...
- 23
2
votes
1
answer
62
views
Counting of zero-modes in conifold theory
I was reading Klebanov and Witten's paper on the conifold theory and at page 11 they state that
[...] In an instanton field of the first $U(N)$ with instanton number $k$, the gluinos of the first $U(...
- 4,120
2
votes
0
answers
56
views
What does it mean to "saturate" an anomaly?
I often see discussion about "saturating" an anomaly in papers having to do with things discrete 't Hooft anomalies, anomaly inflow, and so on. An example (there are many other papers) is ...
- 8,878
2
votes
0
answers
85
views
Peskin and Schroeder perturbative calculation of anomaly
On page 661 Peskin and Schroeder calculates the ABJ anomaly pertubatively. The book gives the ABJ anomly as
$$\tag{19.45}\partial_\mu j^{\mu 5}=-\frac{e^2}{16\pi^2}\epsilon^{\alpha\beta\mu\nu}F_{\...
- 799
1
vote
1
answer
133
views
Classical conservation laws and anomalies in QFT
At the beginning of chapter 4 of the book "Anomalies in quantum field theory" Reinhold Bertlmann, on page 178, the book says:
symmetries: conservation laws are connected with symmetries, ...
- 799
0
votes
1
answer
86
views
Why is $Tr_R(T_a\{T_bT_c\})=-Tr_\overline{R}(T_a\{T_bT_c\})$ for $SU(N)$ representations?
I'm looking at the chiral anomaly in QFT and the term
$$d_{abc}=Tr_R(T_a\{T_b,T_c\})$$
shows up where $Tr_R$ means the trace in the representation $R$, $\overline{R}$ is the conjugate representation ...
- 248
1
vote
0
answers
69
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
5
votes
1
answer
334
views
Free fermion and stress-tensor anomaly
I am trying to compute the (anomalous) transformation law of the free fermion stress-tensor, not with the usual CFT arguments, but by explicit computation.
We can define the classical stress tensor $$...
- 329
1
vote
0
answers
64
views
Chiral anomaly with many fermions with various masses and chiral charges
For a free Dirac fermion of mass $m$ in four dimensions coupled to an external gauge potential $A^\mu(x)$, classical equations of motion for the fermion lead to the equation for the divergence of the ...
- 11
4
votes
0
answers
135
views
Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
- 1,754
3
votes
0
answers
193
views
Witten anomaly and bound states of fermions
In his famous paper "An SU(2) anomaly", Witten begins by noting that an SU(2) gauge theory with a single fermion in the doublet representation is weird, since there is "no obvious ...
1
vote
0
answers
159
views
Anomalies, 2-cocycles and (D+1)-cocycles
I'm learning about anomalies and I'm a bit confused about their relationships to 2-cocycles and 3-cocycles (in the group cohomology $H^{\bullet}(G, U(1))$). The below might only apply to 't Hooft ...
- 143
2
votes
0
answers
82
views
$U(1)_A$ axial anomaly for $SU(N)$ gauge theory in 1+1 dimensions
In massless Abelian gauge theory in 1+1 dimensions, the divergence of axial current is given by
\begin{align*}
\partial_\mu j_A^\mu=\frac{e}{2\pi}\epsilon^{\mu\nu}F_{\mu\nu}=\frac{e}{\pi}F_{01}.
\end{...
- 165
2
votes
0
answers
101
views
Vanishing Chern-Simons partition function
I was reading again the article "Generalized Global Symmetries" and I notice that in the beginning of page 22, they argue that after gauging the $\mathbb{Z}_k$ one-form symmetry, of Chern-...
- 471
1
vote
0
answers
130
views
Anomalous magnetic dipole moment of muon
I'm currently studying for my oral exams and came across exercise 17.1 in Schwartz's Introduction to Quantum Field Theory. In the exercise, we consider the following Lagrangian for super symmetry:
$$\...
- 213
2
votes
0
answers
199
views
Light-cone quantization of open string as derived in Polchinski
Polchinski uses the following gauge conditions, but I don't follow this procedure of gauge fixing and quantization:
\begin{align}
X^+ = \tau, \tag{1.3.8a} \\
\partial_\sigma \gamma_{\sigma \sigma} = 0,...
- 443
0
votes
0
answers
32
views
Why M-theory has eleven dimensions? [duplicate]
Why M-theory has exactly 10+1 dimensions?
Some combinatorics with tensor indices will do.
- 11
3
votes
1
answer
138
views
Complex photon mixed anomaly
$\newcommand{\d}{\mathrm{d}}\newcommand{\U}{\mathrm{U}}\newcommand{\b}[1]{\overline{#1}}\newcommand{\C}{\mathbb{C}}\newcommand{\ex}[1]{\mathrm{e}^{#1}}\newcommand{\i}{\mathrm{i}}$ Consider a free ...
- 4,684
2
votes
1
answer
153
views
Weyl Anomaly for Old Covariant Quantization in String Theory?
In the context of quantization in string theory, the modern approach is the path integral/modern covariant quantization approach. As known from QFT, we fix our gauge and represent the arising Fadeev-...
- 196
0
votes
1
answer
389
views
Chiral symmetry of the Euclidean action for fermions
In the literature, such as QFT Volume-II by Weinberg, p.368, the chiral anomaly is derived using Euclidean path integral. To formulate the question, let's start with the Minkowski space with signature ...
1
vote
1
answer
67
views
Why 't Hooft says: field configuration in Euclidean space that have the vacuum (or a gauge transformation thereof) at the boundary
In Symmetry Breaking through Bell-Jackiw Anomalies G. 't Hooft, Phys. Rev. Lett. 37, 8 – Published 5 July 1976,
't Hooft said that the topological quantum number $n$
$n$ is an integer for all field ...
- 593