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.

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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 ...
Lu Zhang's user avatar
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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)>...
Mohammad Mortezaei Nobahari's user avatar
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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)...
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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)...
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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 (\...
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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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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 $\...
Archie C's user avatar
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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 \ ...
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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 ...
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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 $\{...
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Unitarity of Effective String Theory away from critical dimesions ($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 ...
Mitchell Porter's user avatar
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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 ...
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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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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 ...
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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(...
Davide Morgante's user avatar
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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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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} \...
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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_{\...
Simplyorange's user avatar
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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 ...
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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 ...
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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 ...
AccidentalFourierTransform's user avatar
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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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$U(1)_A$ 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{...
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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-...
Lucas Queiroz's user avatar
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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: $$\...
slowspider's user avatar
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1 answer
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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,...
physicsbootcamp's user avatar
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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.
user1642683's user avatar
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 ...
ɪdɪət strəʊlə's user avatar
2 votes
1 answer
141 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-...
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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 ...
Tuhin Subhra Mukherjee's user avatar
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1 answer
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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 ...
Марина Marina S's user avatar
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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 ...
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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\...
Mouaz Chikhani's user avatar
3 votes
1 answer
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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, ...
Lucas Queiroz's user avatar
1 vote
1 answer
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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 ...
ShoutOutAndCalculate's user avatar
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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 ...
SRS's user avatar
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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 ...
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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. ...
Keith's user avatar
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1 answer
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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 ...
Keith's user avatar
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