All Questions
Tagged with anomaly or quantum-anomalies
393 questions
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Witten anomaly and product representation
The Witten anomaly restricts the number of fermion doublets in an $SU(2)$ theory.
If we have a gauge group $SU(2)_1 \times SU(2)_2$ and have only one fermion fundamental $\psi = (2,2)$, is this theory ...
4
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47
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Resources on Advanced Topics in Standard Model: nonperturbative phenomena, phase transitions, etc
I'm interested in some books on Standard Model physics that discuss advanced topics in quantum field theory. By this I mean topics such as instantons, sphalerons, and friends, the electroweak phase ...
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103
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Anomalies and SPT phases
There seems to be some connection between anomalies and Symmetry Protected Topological Orders, but I cannot find exact details of what the relation is. My impression is that group cohomology and ...
- 178
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40
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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 $U(1)$ $R$-...
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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 ...
- 349
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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.
...
- 111
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2
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159
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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 ...
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82
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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: $$ \frac{n}{...
- 117
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84
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Konishi operator anomalous dimension [closed]
The Konishi operators are operators in the ${\cal N}=4$ SYM theory and are given by:
$$ 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
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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 ...
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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 ...
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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 ($Z$...
- 567
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59
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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?
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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 $\...
- 1,708
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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, $\langle J^\mu J^\nu J^\rho \rangle$, ...
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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 ...
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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}&...
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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
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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 $$i*(<(∂U1/∂kx)| (∂U1/∂ky)>...
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Point-splitting regularization for anomaly in curved spacetime
In flat spacetime, the point-splitting regularization for (chiral) anomaly is discussed in great details in Peskin and Schroeder's QFT.
Does anyone know any good references for calculating anomaly ...
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Axial anomaly for odd dimension
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
- 91
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113
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Axial Chiral Anomaly
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
- 91
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Non-Abelian anomaly: why does non-Hermitian operator have complete basis of eigenvectors?
In section 13.3 of his book [1], Nakahara computes the non-Abelian anomaly for a chiral Weyl fermion coupled to a gauge field by making use of an operator
$$
\mathrm{i}\hat{D} = \mathrm{i}\gamma^\mu (\...
- 2,168
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91
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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 ...
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147
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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 $\...
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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 \ ...
- 1,330
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154
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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 $\{...
- 139
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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 ...
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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 ...
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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 ...
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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 ...
- 1,782
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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
$$\...
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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)
$$
U(2)_L \otimes U(2)_R = SU(2)_L \...
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Counting of zero-modes in conifold theory
I was reading Klebanov and Witten's paper on the conifold theory and at page 11 they state that
[...] In an instanton field of the first $U(N)$ with instanton number $k$, the gluinos of the first $U(...
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What does it mean to "saturate" an anomaly?
I often see discussion about "saturating" an anomaly in papers having to do with things discrete 't Hooft anomalies, anomaly inflow, and so on. An example (there are many other papers) is ...
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Peskin and Schroeder perturbative calculation of anomaly
On page 661 Peskin and Schroeder calculates the ABJ anomaly pertubatively. The book gives the ABJ anomly as
$$\tag{19.45}\partial_\mu j^{\mu 5}=-\frac{e^2}{16\pi^2}\epsilon^{\alpha\beta\mu\nu}F_{\...
- 859
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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, ...
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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
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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\...
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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 $$...
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Chiral anomaly with many fermions with various masses and chiral charges
For a free Dirac fermion of mass $m$ in four dimensions coupled to an external gauge potential $A^\mu(x)$, classical equations of motion for the fermion lead to the equation for the divergence of the ...
- 11
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141
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Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
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Witten anomaly and bound states of fermions
In his famous paper "An SU(2) anomaly", Witten begins by noting that an SU(2) gauge theory with a single fermion in the doublet representation is weird, since there is "no obvious ...
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Anomalies, 2-cocycles and (D+1)-cocycles
I'm learning about anomalies and I'm a bit confused about their relationships to 2-cocycles and 3-cocycles (in the group cohomology $H^{\bullet}(G, U(1))$). The below might only apply to 't Hooft ...
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89
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$U(1)_A$ axial anomaly for $SU(N)$ gauge theory in 1+1 dimensions
In massless Abelian gauge theory in 1+1 dimensions, the divergence of axial current is given by
\begin{align*}
\partial_\mu j_A^\mu=\frac{e}{2\pi}\epsilon^{\mu\nu}F_{\mu\nu}=\frac{e}{\pi}F_{01}.
\end{...
- 173
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Vanishing Chern-Simons partition function
I was reading again the article "Generalized Global Symmetries" and I notice that in the beginning of page 22, they argue that after gauging the $\mathbb{Z}_k$ one-form symmetry, of Chern-...
- 471
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148
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Anomalous magnetic dipole moment of muon
I'm currently studying for my oral exams and came across exercise 17.1 in Schwartz's Introduction to Quantum Field Theory. In the exercise, we consider the following Lagrangian for super symmetry:
$$\...
- 213
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212
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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,...
- 453
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33
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Why M-theory has eleven dimensions? [duplicate]
Why M-theory has exactly 10+1 dimensions?
Some combinatorics with tensor indices will do.
- 11
3
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1
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143
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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 ...
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