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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Feynman graph of induced current

I'm self studying QFT from Peskin and Schroeder. In chapter 19 of this book, page 653 (Perturbation theory anomalies)the expectation value of the induced current is calculated. I'm confused with the ...
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1answer
47 views

Global Anomaly and Ward Identity

This question is a continuation of the answer posted for this question about anomalies. What happens to the Ward identity corresponding to a global symmetry if that symmetry is anomalous? I mean, is ...
2
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1answer
32 views

Computation of theta-term from triangle diagram

The chiral $U(1)$ anomaly in QCD can be calculated exactly by one-loop Feynman diagrams, for example by the famous triangle diagram. I am currently performing the computation to get a better ...
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1answer
61 views

What is the axial current?

The axial current is defined as $$j^\mu_5 = \bar{\psi} \gamma^\mu \gamma_5 \psi.$$ This quantity is important when studying anomalies. Explicitly working out components, the axial current is just the ...
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33 views

The scale anomaly and dependence on scale

The scale anomaly states that if we have renormalizable theory without dimensionful function, which is scale invariant, then corresponding quantum theory may lost this symmetry because of ...
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1answer
66 views

Baryon number violation in the Standard Model

Anomaly cancellation in the Standard model requires $B-L$ to be constant, which is done using perturbative diagrammatic expansion. Secondly, baryon number is conserved as an $U(1)$ global field ...
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2answers
95 views

Anomalous Slavnov-Taylor identity

I will be happy if someone could clarify the mystery here. Consider the following derivation of the anomalous Slavnov-Identity. It's based on lecture notes by Adel Bilal. Suppose we have an action ...
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2answers
178 views

Quantum Anomalies and Quantum Symmetries

In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be ...
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49 views

Are SUSY transformations free from anomalies?

Although I've studied supersymmetic field theories for several years, there is a fundamental problem annoying me: Do SUSY transformations (including both the ordinary ones in various dimensions and ...
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42 views

What is the simplest chiral $U(1)$ theory that satistifies both gauge and gravity anomalies?

I've learned the chiral $U(1)$ theory that satisfies either gauge anomalies or gravity anomalies. But what's the theory satisfies both of them?
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49 views

How to visualize a sphere bundle?

In the paper ``Gravitational Anomaly Cancellation for M Theory Fivebranes", the authors consider removing a tubular region of radius $\epsilon$ around the M5 brane (in order to make sense of the three ...
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43 views

Non-zero gravitational anomaly

Analogous to the Adler-Jackiw-Bell anomaly of QCD, we have an anomaly in gravity when we consider gravity to be coupled to chiral fermions: \begin{equation} \partial_\nu J^\nu_5\propto R\tilde{R}, ...
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74 views

Why is it that the conformal anomaly has to be scale invariant?

When reading about conformal anomalies, such as in this paper it is often stated that the anomaly (ie. $ \delta W[g]/ \delta \sigma$ where $ W[g]$ is the quantum effective action for gravity) must be ...
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Anomalies, neutrino condensate and neutrino masses

Is neutrino number conservation not affected by the U(1) QCD and QED anomalies due its zero U(1) charge? Is this the reason why the neutrino should be massless and there should be no lepton family ...
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22 views

QCD condensate and lepton mass

I read that the QCD U(1) anomaly is caused by the QCD condensate giving rise to quark masses. Does the QCD condensate also give masses to leptons (electron, mu, tau, neutrinos), or are these masses ...
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41 views

Chiral anomaly and fermion number conservation

Chiral anomalies in QED and QCD violate fermion number conservation, since a U(1) vector symmetry corresponds to fermion number conservation. However, only the LH and RH fermion numbers are not ...
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48 views

M5 brane zero modes

The Euclidean M5 brane worldvolume has an anti self-dual 3-form and two negative chirality spinors. The spinors can couple to the SO(5) gauge fields of the normal bundle, but the 3-form cannot couple ...
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1answer
184 views

Anomaly cancellation in the standard model (calculating the symmetrized trace of generators)

The Problem We can show that the condition for the Standard Model to be anomaly-free is that the symmetrized trace over the generators of the gauge group vanishes: \begin{align} \text{tr} ...
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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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146 views

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
166 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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1answer
63 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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107 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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302 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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196 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
181 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
501 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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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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62 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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68 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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152 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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2answers
196 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
114 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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28 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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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
77 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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63 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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1answer
333 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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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
153 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
81 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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2answers
494 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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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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199 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
124 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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693 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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0answers
166 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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272 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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355 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
224 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 ...