This tag is for anomalies in a symmetry, either in classical or quantum theories. This tag should **not** be used for anomalies in a measurement.

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Target Space Lorentz Invariance vs. World Sheet Weyl Invariance

The Polyakov action, $S\sim \int d^2\sigma\sqrt{\gamma}\, \gamma_{ab}\partial^a X^\mu \partial ^b X_\mu$, has the well known classical symmetries of world sheet diffeomorphism invariance, world ...
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QED and anomaly

I've just started to learn anomalies in quantum field theories. I have a question. How to show that QED is free from vector current anomaly and what would happen if it were not? In other words, how ...
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1answer
74 views

Consequences of local and global anomaly

Are the physical consequences of anomalies associated with a local symmetry is different from that of a global symmetry? If yes, why? We have global anomaly in the standard model but not local ...
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32 views

Can the effective vertex for $\gamma\to3\pi$ be derived directly from the anomaly?

My question is whether the effective vertex for $\gamma\to3\pi$ can be derived directly from the anomaly (given in the first equation below), in analogy with the $\pi^0\to2\gamma$ vertex? As far as I ...
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40 views

Nature of the Wess-Zumino term in an effective field theories

Let's have theory involves fermions which interact through spontaneously broken (by field $g = ve^{i\theta }$ value $v$) $U(1)$ group, and then to integrate fermions out. Will Wess-Zumino term $$ ...
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119 views

Effective field theories and gauge anomalies cancellation

Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
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78 views

What is the reason for chiral anomalies in condensed matter systems?

If you consider a massless relativistic fermion theory and you perform a chiral transformation, then you realize that while the classical action remains invariant under this transformation the ...
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1answer
75 views

Point splitting technique in Pesking and Schroeder

One of the cornerstones of point splitting technique of calculating chiral anomaly (Peskin and Schroeder 19.1, p.655) is a symmetric limit $\epsilon \rightarrow 0$. And this is the point that I don't ...
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1answer
200 views

Chiral anomaly in Weyl semimetal

In the presence of electromagnetic fields $E$ and $B$, four current is not conserved in a Weyl semimetal i.e. $\partial_{\mu} j^{\mu}\propto E\cdot B \neq 0$. There are some proofs in the literature ...
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47 views

Fujikawa's method for 2+1-dimensional parity anomaly?

Fujikawa's chiral rotation method is applied to calculate 3+1 dimensional chiral anomaly in many textbooks, but is there any counterpart of that method in deriving 2+1 dimensional parity anomaly, i.e. ...
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51 views

Anomaly and Weyl spinors

I try to better understand anomalies in QFT and I've got a question concerning derivation of axial anomaly in Terning's lectures (page 12) Consider a theory of Weyl fermions coupled to a gauge field ...
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43 views

A question on intermediate step in deriving gravitational anomaly by Fujikawa's method

In Fujikawa's 'Path integrals and Quantum Anomalies', Eq.(10.26) in the derivation of gravitational anomaly in Chapter 10.1 is puzzling for me. ...
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94 views

Anomaly for Majorana fermion?

In 4-spacetime dimension, is there U(1) gauge field chiral anomaly associated with Majorana fermion (or I am not sure if it is equivalent, majorana representation)? Besides, I have read from several ...
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1answer
79 views

Is there a 2D manifold on which the Dirac equation has a zero mode?

The two-dimensional (2D) Dirac equation $(\sigma_1iD_1+\sigma_2 iD_2)\psi=E\psi$ admits zero mode ($E=0$) solutions on a non-trivial gauge background, such as the zero mode at the core of a U(1) gauge ...
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1answer
76 views

Polyakov equation in the strings theory

In the equation of Polyakov there wouldn't be in our universe 10 or 11 dimensions but more (26) because it is referred to the bosonic theory. Are there any connections between this equation and the ...
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18 views

Few questions about SM baryogenesis

SM provides baryogenesis via leptogenesis due to anomalies and sphaleron processes. I have a few questions on it. How exactly the anomalies in lepton and baryon currents provide convertation of ...
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39 views

Fujikawa method for arbitrary transformations

When the Fujikawa method is presented in every book I've read so far, the transformation is initially written as $e^{i\chi (x) \gamma^{5}}$. The trace of $i\chi(x)\gamma^{5}$ is done by including a ...
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1answer
41 views

Sphaleron interactions erase baryon asymmetry?

The sphaleron interactions in the standard model is $(B-L)$ conserving and $(B+L)$ violating. Each sphaleron transition causes $\Delta B$ and $\Delta L$ to change by the same amount so that ...
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35 views

Specific Reference for 't Hooft Anomaly Matching Condition

Does anyone know, in exactly which paper did G.'t Hooft "propose" anomaly matching condition? I scrambled across his list of publications, but I am unable to make out.
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317 views

anomalous chiral symmetry and the $\bar\theta$ parameter

I am studying anomalous $U(1)$'s, related to the strong CP problem, and I have some trouble with the origin of the parameter $\bar{\theta}$. We start with the QCD Lagrangian with the topological ...
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153 views

Why is it important that the vector current should be conserved in QED?

In Quantum Field Theory and the Standard Model by MD Schwartz in the chapter about the anomalies, he derives from the equation of motions and the Noether currents of a effective massless QED ...
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1answer
109 views

The index of a Dirac operator and its physical meaning

I recently read Witten's paper from the 1980s and he often uses the notion of the index of a Dirac operator in K-theory. What is the meaning of the index of a Dirac operator? What exactly is the ...
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1answer
70 views

What are the two dimensions of relativity that are added to string theory?

Based on the Ramanujam's modular functions, somehow these magic numbers 10 and 26 spacetime dimensions appear in string theory. The dimensions can be viewed as 8 + 2 and 24 + 2. The number 2 is added ...
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170 views

What is the difference between Chiral anomaly, ABJ anomaly, and Axial anomaly?

I get confuse with these three terms: Chiral anomaly, ABJ anomaly, and Axial anomaly. I can not find standard definition of these three. Is there anyone can describe precisely?
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62 views

How to solve the following set of equations (magnetohydrodynamics with anomaly term)?

Let's have system of equations: $$ \tag 1 [\nabla \times \mathbf E^{(1)}(\mathbf r , t) ] = -\frac{\partial \mathbf B^{(1)}(\mathbf r , t)}{\partial t} , $$ $$ \tag 2 [\nabla \times \mathbf ...
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146 views

Confusion about two definitions of anomalies

As I am currently studying for an exam about quantum field theory and string theory, I got confused about the notion of "anomalies" and how they are actually defined. Similar questions have already ...
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1answer
85 views

Significance of total divergence anomaly term

What is the significance of the fact that the anomany term (calculated from the triangle diagram) is a total divergence? Or, in other words, what is the significance of $$\partial_\mu j^\mu_A\sim ...
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403 views

Chiral anomalies

Recently I have read that there is contraction of chiral anomalies in SM. But people are working on chiral anomalies theory. So I have the question: what is the importance of development of the theory ...
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143 views

Anomalies in QFT books

Why in most QFT books when author discusses of non-invariance of measure of path integral (massless fermions interact with gauge fields) $$ \int D\bar{\Psi} D\Psi \to |\Psi \to U\Psi , \quad ...
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189 views

Chiral Anomaly in Massless QED

Classical massless QED has axial current conservation. When quantizing the theory, we expect that suddenly $\partial_\mu \hat{j}^{\mu5}\neq0$ (as an operator equality). I have two questions regarding ...
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315 views

Quantum symmetries that are not classical symmetries

An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing ...
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1answer
141 views

Why is baryon or lepton violation in standard model is a non-perturbative effect?

The baryon number B or lepton number L violation in the standard model arise from triangle anomaly. Right? Triangle diagrams are perturbative diagrams. Then why the B or L violation in Standard model ...
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1answer
179 views

$U(1)$ abelian/axial/chiral anomaly in 4D

I am reading $U(1)$ abelian/axial/chiral anomaly in 3+1 dimensions using the path integral method (Fujikawa). Am I wrong in assuming that the anomaly can be cancelled by introducing a counter term in ...
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2answers
162 views

Traces in different representation

I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental ...
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1answer
335 views

What exactly is a gauge anomaly?

In lots of papers I read about gauge anomalies. For example, avoiding gauge anamolies in the MSSM is the reason for introducing an extra Higgs doublet. Gauge anamolies in the Standard Model are ...
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1answer
131 views

Choice of basis for Fujikawa method to derive chiral anomaly

I am studying the Fujikawa method of determining the chiral anomalies in a $U(1)$ theory. As we know the basis vectors selected are the eigenstates of the Dirac operator. One of the reasons given is ...
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A question about the Henningson-Skenderis holographic Weyl anomaly calculation.

I am referring to this very famous paper. http://arxiv.org/abs/hep-th/9806087 I am referring to equations 20 and 27 and 28. Anyone can help derive them? I vaguely think that they substituted ...
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1answer
267 views

Conformal/trace anomaly and index theorem

I am reading the chapters on characteristic classes and the index theorems in Nakahara. It is proven in the text that any chiral or gravitational anomaly $\mathcal{A}$ is given by $$\mathcal{A}=\int ...
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Anomalies from a Renormaization Group Equation (RGE)

This is an approach to anomalies which seems unfamiliar to me.. Firstly what is this function $W$ which seems to satisfy the equation, $\frac{\partial W }{\partial g^{\mu \nu} } = \langle T_{\mu ...
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114 views

Why is the chiral symmetry $SU(2)_A$ not anomalous?

Using Fujikawa's path integral treatment of the triangle diagram, one can show that $$\mathrm{Tr} \gamma^5 = \int d^4 x\ \partial_{\mu}j^{\mu} $$ Where $j^{\mu}$ is the Noether current of $U(1)_A$. ...
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1answer
85 views

$P$ symmetry that is apparent with one definition of fields but not with another

Suppose that we have a Lagrangian density like $$\mathcal L = -\frac{1}{4} \operatorname{tr} F_{\mu\nu}F^{\mu\nu} + \frac{\theta}{32\pi^2} \operatorname{tr} \big( \epsilon^{\mu\nu\rho\sigma} ...
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151 views

Gravitational anomalies and topological order

I wonder the relation of gravitational anomaly and topological order. Specifically: What is the definition of gravitational anomaly here? How are they related?
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98 views

Hamiltonian Operator Interpretation of Quantum Anomaly

We can see the definition of quantum anomaly in terms of Lagrangian path integral formulation. What is the definition of quantum anomaly in terms of Hamiltonian operator approach or even more directly ...
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159 views

Help in deriving the Adler-Bell-Jackiw anomaly

I'm stuck on the derivation of the Adler-Bell-Jackiw anomaly. This is discussed on page 666 of Peskin and Schroeder (equation 19.76) or these notes on page 14 (equation 39). According to these ...
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217 views

Quantum Anomalies for Bosons

We know that there is Adler and Bell-Jackiw(ABJ) type anomalies for fermions. In some case, the ABJ anomaly affecs particle physics pheonomelogy, such as pion decays or kaon decays(in the case of ...
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Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
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2answers
858 views

Symmetries of the Standard Model: exact, anomalous, spontaneously broken

There are a number of possible symmetries in fundamental physics, such as: Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and ...
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131 views

Anomaly cancellation and fermion number violation

In the standard model, an axial $SU(3)$ currents has anomaly which after quantization leads to the fermion number violation. However, taking all the fermions into account we note that the anomalies ...
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166 views

Zumino's consistent and covariant anomalies - applied to quantum hall?

What is the `physical' meaning of consistent anomalies and covariant anomalies? Perhaps a good Reference is: Consistent and covariant anomalies in gauge and gravitational theories - William A. ...
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160 views

Some fundamental results in QFTs [closed]

In quantum theory we have some principles that guides us, e.g. Pauli's principle. What I am after in this question is a list of fundamental results, be it equation or identities that must hold in a ...