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.
380
questions
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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 ...
0
votes
0
answers
27
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 $$i*(<(∂U1/∂kx)| (∂U1/∂ky)>...
0
votes
0
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69
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Point-splitting regularization for anomaly in curved spacetime
In flat spacetime, the point-splitting regularization for (chiral) anomaly is discussed in great details in Peskin and Schroeder's QFT.
Does anyone know any good references for calculating anomaly ...
1
vote
0
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30
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Axial anomaly for odd dimension
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
2
votes
0
answers
96
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Axial Chiral Anomaly
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
1
vote
1
answer
71
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Non-Abelian anomaly: why does non-Hermitian operator have complete basis of eigenvectors?
In section 13.3 of his book [1], Nakahara computes the non-Abelian anomaly for a chiral Weyl fermion coupled to a gauge field by making use of an operator
$$
\mathrm{i}\hat{D} = \mathrm{i}\gamma^\mu (\...
3
votes
0
answers
67
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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 ...
0
votes
1
answer
109
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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 $\...
3
votes
1
answer
112
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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 \ ...
0
votes
0
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63
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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 ...
2
votes
1
answer
110
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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 $\{...
1
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0
answers
56
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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 ...
1
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0
answers
108
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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 ...
1
vote
0
answers
36
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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 ...
1
vote
1
answer
168
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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 ...
9
votes
2
answers
730
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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
$$\...
2
votes
0
answers
59
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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)
$$
U(2)_L \otimes U(2)_R = SU(2)_L \...
0
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0
answers
65
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Can this SUSY anomaly disappear in higher dimensions?
I read this thread of articles by Casher(quite marginal in terms of citation) where they show in certain realistic models SUSY is broken by non-perturbative effects.
Explicit breaking of supersymmetry ...
2
votes
1
answer
59
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Counting of zero-modes in conifold theory
I was reading Klebanov and Witten's paper on the conifold theory and at page 11 they state that
[...] In an instanton field of the first $U(N)$ with instanton number $k$, the gluinos of the first $U(...
2
votes
0
answers
51
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What does it mean to "saturate" an anomaly?
I often see discussion about "saturating" an anomaly in papers having to do with things discrete 't Hooft anomalies, anomaly inflow, and so on. An example (there are many other papers) is ...
1
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0
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37
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Conservation of classical currents in an interacting fermionic model
I have a system of massless fermions described by
\begin{equation}
Z = \int {\cal D}\psi {\cal D} \overline{\psi} e^{S_{\alpha}}
\end{equation}
where $S_{\alpha} = \int d^{2}x [i\overline{ \psi} \...
2
votes
0
answers
71
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Peskin and Schroeder perturbative calculation of anomaly
On page 661 Peskin and Schroeder calculates the ABJ anomaly pertubatively. The book gives the ABJ anomly as
$$\tag{19.45}\partial_\mu j^{\mu 5}=-\frac{e^2}{16\pi^2}\epsilon^{\alpha\beta\mu\nu}F_{\...
1
vote
1
answer
128
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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, ...
0
votes
1
answer
80
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 ...
1
vote
0
answers
48
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\...
5
votes
1
answer
303
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 $$...
1
vote
0
answers
51
views
Chiral anomaly with many fermions with various masses and chiral charges
For a free Dirac fermion of mass $m$ in four dimensions coupled to an external gauge potential $A^\mu(x)$, classical equations of motion for the fermion lead to the equation for the divergence of the ...
4
votes
0
answers
123
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Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
3
votes
0
answers
162
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Witten anomaly and bound states of fermions
In his famous paper "An SU(2) anomaly", Witten begins by noting that an SU(2) gauge theory with a single fermion in the doublet representation is weird, since there is "no obvious ...
1
vote
0
answers
130
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Anomalies, 2-cocycles and (D+1)-cocycles
I'm learning about anomalies and I'm a bit confused about their relationships to 2-cocycles and 3-cocycles (in the group cohomology $H^{\bullet}(G, U(1))$). The below might only apply to 't Hooft ...
2
votes
0
answers
70
views
$U(1)_A$ axial anomaly for $SU(N)$ gauge theory in 1+1 dimensions
In massless Abelian gauge theory in 1+1 dimensions, the divergence of axial current is given by
\begin{align*}
\partial_\mu j_A^\mu=\frac{e}{2\pi}\epsilon^{\mu\nu}F_{\mu\nu}=\frac{e}{\pi}F_{01}.
\end{...
2
votes
0
answers
87
views
Vanishing Chern-Simons partition function
I was reading again the article "Generalized Global Symmetries" and I notice that in the beginning of page 22, they argue that after gauging the $\mathbb{Z}_k$ one-form symmetry, of Chern-...
1
vote
0
answers
105
views
Anomalous magnetic dipole moment of muon
I'm currently studying for my oral exams and came across exercise 17.1 in Schwartz's Introduction to Quantum Field Theory. In the exercise, we consider the following Lagrangian for super symmetry:
$$\...
2
votes
1
answer
152
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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,...
0
votes
0
answers
32
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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.
3
votes
1
answer
134
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 ...
2
votes
1
answer
135
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-...
0
votes
1
answer
292
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
62
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 ...
1
vote
0
answers
194
views
Axions as goldstone bosons of anomalous $U(1)$ symmetry
In the $m_q \rightarrow 0$ limit the QCD lagrangian has the symmetry $U(N)_V \times U(N)_A$. Including just the two lightest quarks, $N=2$, and looking at the $U(2)_A=SU(2)_A \times U(1)_A$ part, we ...
4
votes
0
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150
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Why does Tong uses Euclidean Gamma matrices in this step of deriving the Chiral Anomaly?
In David Tong's GT notes on page 137, he uses the trace identity for Euclidean gamma matrices given by
$$\text{Tr}(\gamma^5\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma})=4\epsilon^{\mu\nu\rho\...
3
votes
1
answer
142
views
Apparent elimination of a 't Hooft anomaly in quantum spin system
The simplest system with a 't Hooft anomaly is the spin $\frac{1}{2}$ system with hamiltonian $\hat{H}=0$. The 't Hooft anomaly follows from the fact that such system has a trivial $SO(3)$ symmetry, ...
1
vote
1
answer
119
views
How did the two copies of the Witt algebra become two copies of the Virasoro algebra in the CFT?
The Virasoro algebra
\begin{equation}
[L_m,L_n]=(m-n) L_{m+n} +\frac{c}{12} (m^3-m) \delta_{m+n,0}
\end{equation}
of the stress energy tensor $T$ was said to follow from the witt algebra of the local ...
2
votes
0
answers
145
views
Anomalous baryon current in the Standard Model (SM) and the stability of free protons within the confines of the SM
In the Standard Model, the baryon number is not exactly conserved due to anomaly but the decay rate is extraordinarily small at ordinary temperatures. Does this make free protons unstable in the ...
2
votes
0
answers
62
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How does one arrive at the relation of commutator $\left[M^{-i}, M^{-j}\right]$ of Lorentz generators $M^i$ in terms of the string modes $\alpha_n^i$?
I am reading the book "String theory demystified" by David McMahon.
On page 149, the author discusses the "critical dimension" for superstrings.
the number of spacetime dimensions ...
2
votes
1
answer
76
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In calculating the abelian anomaly, why can't we use $D^\mu D_\mu$ as a regulator? - Weinberg QFT vol 2 p.364
In calculating the abelian anomaly of gauge theories based on the method by Fujikawa, the square of the Dirac operator, $(D^\mu \gamma_\mu)^2$, is used. Here $D^\mu$ is the gauge covariant derivative.
...
1
vote
1
answer
97
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A question about the Dirac operator and zero modes in the book "Mirror Symmetry" by Clay Institute
I have a question about the book "Mirror Symmetry" p.296~298.
Using the notations there, the Dirac operator and its conjugate are denoted as $D_z$ and $D_{\overline{z}}$. In p.297, the book ...
14
votes
3
answers
3k
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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 ...
4
votes
0
answers
179
views
Stress tensor trace anomaly in two dimensions
I'm trying to calculate the expectation value of the stress tensor in 2D following the book "Quantum fields in curved space" (Birrell and Davies). In 2D the divergent contribution to the one-...
0
votes
1
answer
177
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Gauge anomalies?
Why are gauge anomalies so important for any model?
Secondly, any model has to respect the gauge anomalies cancellation requirement?
If this isn't true, then why does one check their model to look ...