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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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 ...
1
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1answer
62 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 ...
2
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0answers
33 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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48 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 ...
9
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1answer
106 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 ...
2
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1answer
53 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 ...
5
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1answer
137 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 ...
2
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0answers
106 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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0answers
93 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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0answers
174 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 ...
1
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1answer
101 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 ...
4
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1answer
117 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 ...
2
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1answer
158 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 ...
3
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1answer
59 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 ...
2
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0answers
32 views

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 ...
12
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1answer
224 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 ...
2
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0answers
55 views

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 ...
7
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1answer
91 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 $U(1)_A$. ...
6
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1answer
79 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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0answers
59 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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0answers
82 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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0answers
106 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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1answer
119 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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58 views

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
740 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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113 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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0answers
122 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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158 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 ...
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2answers
234 views

For the $U(1)$ problem, is the Kugo and Ojima Goldstone quartet wrong?

On page 96 in "Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem", Prog. Theor. Phys. Suppl. 66 (1979) 1, KO state the following: Finally we should ...
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0answers
132 views

Anomalous dimensions in the $O(N)$ model

Is there any statement known about the anomalous dimensions of the $O(N)$ model in various dimensions and/or in the large-N limit? If a $\phi^4$ ("double-trace") term is coupled to an $O(N)$ model ...
3
votes
1answer
170 views

Ambiguity in Beta Functions (2-loop)

Beyond one-loop, the beta function of a QFT is scheme dependent. I would like to understand better this ambiguity. The easiest thing to say is that you haven't calculated something physical, so of ...
6
votes
2answers
220 views

Anomalies and Modification of symmetry algebra

This question is motivated by 2-dimensional CFTs where the Classical conformal group (defined by the Witt algebra) is modified to the Virasoro algebra in the quantum theory. In this question, it was ...
8
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2answers
393 views

Central charge in a $d=2$ CFT

I've always been confused by this very VERY basic and important fact about two-dimensional CFTs. I hope I can get a satisfactory explanation here. In a classical CFT, the generators of the conformal ...
6
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2answers
270 views

Quantum Anomalies in Non-Gauge Theories?

I'm reading about quantum anomalies in QFT and all the examples seem to arise in gauge theories. Is it true that theories without a local gauge invariance don't have quantum anomalies? I can't think ...
9
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1answer
266 views

Anomalies for not-on-site discrete gauge symmetries

If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
8
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1answer
288 views

About the general expression of trace anomaly and CFT partition functions

I have put up a question here, http://mathoverflow.net/questions/139685/proof-of-the-general-expression-for-anomaly-in-a-cft-and-its-partition-function Here I am putting up a slightly different ...
6
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2answers
924 views

The phrase “Trace Anomaly” seems to be used in two different ways. What's the relation between the two?

I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing. The first way I've seen it used is in the manner, for ...
8
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1answer
463 views

Why does tachyon arise in bosonic string theory?

I am looking for precise mathematical and physical reasons which cause the presence of tachyon in bosonic string theory(specially closed bosonic string theory). Has it to do with the specific form of ...
7
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2answers
287 views

On the Axial Anomaly

I know that if we start with a massive theory, the chiral states $L$ and $R$ remain coupled to each other in the massless limit. Because a charged Dirac particle of a given helicity can make a ...
5
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1answer
372 views

Is this explanation of “Why nine space dimensions?” correct?

In Gordon Kane's Supersymmetry and Beyond (p. 118), he states: String theory has to be formulated in nine space dimensions or it is not a consistent mathematical theory. There doesn't seem to be a ...
6
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1answer
171 views

Critical dimension in quantization of p-branes

So I have what might be a fairly basic question, but my understanding that in the quantization of the the string, or the 1-brane, there are conditions on the number of spacetime dimensions to ensure ...
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3answers
515 views

Homotopy $\pi_4(SU(2))=\mathbb{Z}_2$

Recently I read a paper using $$\pi_4(SU(2))=\mathbb{Z}_2.$$ Do you have any visualization or explanation of this result? More generally, how do physicists understand or calculate high dimension ...
9
votes
1answer
421 views

why are two higgs doublets required in SUSY?

I can't really understand why two higgs doublets are required in SUSY. From the literature, I have found opaque explanations that say something along the lines of: the superpotential W must be a ...
6
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1answer
351 views

Chiral anomaly in odd spacetime dimensions

In odd number of space-time dimensions, the Fermions are not reducible (i.e. do not have left-chiral and right-chiral counterparts). Does this mean that there is no such thing as 'chiral' anomalies ...
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170 views

Why does renormalization need an unbroken symmetry?

Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
5
votes
1answer
641 views

simple explanation of chiral anomaly?

Can somebody provide a fairly brief explanation of what the chiral anomaly is? I have been unable to find a concise reference for this. I know QFT at the P&S level so don't be afraid to use math.
12
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2answers
519 views

If gauge symmetries are fake, then why do we care if they are anomalous?

My understanding is that gauge symmetries are fake in that they are only redundancies of our description of the system that we put in (either knowingly or unknowingly) see Gauge symmetry is not a ...
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1answer
323 views

what is the relationship between these two sorts of anomalies?

Recently there has been a few questions about anomalies in QFTs: Why do some anomalies (only) lead to inconsistent quantum field theories Classical and quantum anomalies In these, people have been ...
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2answers
844 views

Why do some anomalies (only) lead to inconsistent quantum field theories

In connection with Classical and quantum anomalies, I'd like to ask for a simple explanation why some anomalies lead to valid quantum field theories while some others (happily absent in the standard ...
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2answers
2k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views: Anomalies are due to the fact that quantum field ...