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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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1answer
79 views

Are anomalies always undesirable?

In the glossary of the AMS book on Quantum Fields and Strings it is stated that An anomalous theory does not make sense quantum mechanically, so anomaly cancellation is a fundamental requirement ...
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99 views

Is it possible to couple an odd number of Dirac fermions, at finite density, to a massless gauge field in 2+1d?

In a beautiful paper by A. N. Redlich (PRL $\bf{52}$, 18 (1984)) on the parity anomaly, the author indicates that an odd number of Dirac fermions can never be coupled to a massless gauge field in 2+1d ...
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29 views

Trouble Understanding Computation in Weinberg Quantum Theory of Fields Vol. 2 Chapter 22

In Chapter 22 (Anomalies) of Weinberg Vol. 2, the author is evaluating the anomaly function $\mathcal{A}(x) = -2[Tr(\gamma_5 t f(-(\not{D}/M)^2))\delta(x-y)]_{y\rightarrow x}$, following Fujikawa'...
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30 views

Showing that $U(1)_R$ charge is non-anomalous in SUSY QCD when $r=\frac{F-N}{F}$

I'm trying to show that the value of the R-charge $r$ for which the R-symmetry is non-anomalous is given by $r=\frac{F-N}{F}$. To do this we must calculate the triangle diagrams for the quarks $\...
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22 views

What is the critical string?

What is the critical string? From wiki, I found the definition of non-Critical string wiki The non-critical string theory describes the relativistic string without enforcing the critical ...
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1answer
59 views

$SU(5)$ representation and higher anti-symmetric traces

In Zee QFT book v2 p.411 eq.16-17, he shows the SU(5) gauge theory anomaly cancellation by the following: The 1st line in fundamental of SU(5) $$ tr(T^3)=3(+2)^3+2(-3)^3=30, $$ is easy to follow, ...
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67 views

Mathematics of Anomalies in QFT

As a mathematics student interested in theoretical physics, I found it very hard to study about anomalies in QFT in standard physics texts. They concentrate on particular examples (like chiral anomaly)...
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2answers
536 views

Can anomalies exist without gauge fields?

In Schwartz's QFT book, it is stated that anomalies cannot exist in a theory without gauge fields. This is because anomalies always give equations like $$\partial_\mu j^\mu \sim F \tilde{F}$$ where ...
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0answers
62 views

What's the real resolution of the $U(1)_A$ problem?

To recap the problem, consider QCD with three massless quark flavors. There is a symmetry $$SU(3)_L \times SU(3)_R \times U(1)_L \times U(1)_R$$ corresponding to independent rotations of the left-...
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1answer
60 views

What happens to the $U(1)_B U(1)_Y^2$ anomaly in the Standard Model?

Baryon number $U(1)_B$ is anomalous in the Standard Model, as can be seen by computing a $U(1)_B SU(2)_L^2$ triangle diagram. This implies that $$\partial_\mu J^{\mu B} \sim W_{\mu\nu} \tilde{W}^{\mu\...
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Gauging $U(1)_{B-L}$ in the absence of right-handed neutrinos

If we gauge the baryon minus lepton number symmetry $U(1)_{B-L}$, the mixed lepton-gravity-anomalies cancel in the presence of right-handed neutrinos (see e.g. this paper). However, if right-handed ...
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1answer
104 views

2D anomaly-free condition for a gauge theory

Take a $SU(2)$ gauge theory in 2d spacetime, say there are $n_1$ left-handed Weyl fermion in spin-1 written as $$ 1_L, $$ and $n_0$ left-handed Weyl fermion in spin-0 written as $$ 0_L . $$ and $n_{1/...
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1answer
69 views

Equality of positron and proton charge problem statement

When I hear that the equality of positron and proton charge is an unsolved problem I assume that we are putting the electric charge by hand in the electroweak section of the SM Lagrangian. Is this ...
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0answers
46 views

$Z_1=Z_2$ without Ward-Takahashi identity?

In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...
2
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1answer
73 views

Simple explanation of the QCD VEV in terms of instantons

I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
2
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0answers
42 views

Feynman rules for anomalous vertex [closed]

We can read Feynman rules directly from the lagrangian in the simplest cases, but for the following lagrangian I am a few stuck $\mathcal{L}=4g\phi\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}A_{\nu}\...
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65 views

Gauge anomaly from conformal dimension?

According to ref.1, the Chern-Simons theory $\mathrm{SU}(N)_k$ has a $\mathbb Z_N$ one-form symmetry with anomaly $$ \eta=\exp\left[-2\pi i \frac{k}{N}\right]\tag{4.12} $$ which, apparently, can be ...
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0answers
30 views

Dimensions and superstring theory [duplicate]

While I was reading B. Greene 's "the fabric of the cosmos" , There he says that the theory of relativity and quantum mechanics are the two pillars on which modern physics stands, but these theories ...
3
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1answer
79 views

Does the ABJ anomaly for the Abelian gauge field have a topological argument?

We known that the ABJ anomaly for non-abelian gauge fields with gauge group containing $SU(2)$ as a subgroup has a topological argument from the Euclidean path integral. Through studying the Euclidean ...
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1answer
45 views

Proposal of the Virasoro modes and algebra

Hi I am wondering what the first published paper on Virasoro modes was? And what about Virasoro algebra?
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76 views

Energy-Momentum Tensor and Variation of the Partition Function

I am currently working through the Fujikawa paper "Comments on Chiral and Conformal Anomalies". I have, however, had some issues getting around some notation, and perhaps a little of the logic, he ...
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1answer
126 views

Can a gauge anomaly be *removed* by quantum corrections?

Consider a classical gauge field coupled to a vector field $j^\mu$. Gauge invariance requires that $\mathcal A_\mathrm{cl}:=\partial_\mu j^\mu$ vanishes: $$ \mathcal A_\mathrm{cl}\equiv 0 $$ In other ...
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120 views

Can cut-off regularisation cause a Poincaré anomaly?

Momentum cut-off regularisation leads to non-covariant results, i.e., it breaks the Poincaré covariance of the theory. Is there any guarantee that Poincaré covariance is always restored when we remove ...
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130 views

Why does M-theory need 11 dimensions? [duplicate]

I have looked on the internet and no one can tell me why M-theory needs eleven dimensions?
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1answer
82 views

Parity Invariance of Path-Integral Measure

If a theory is parity invariant classically, is its path-integral measure also invariant under parity?
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26 views

Can quantum anomalous hall effect in ferromagnetic material be attribute to the internal B field?

I have learned that the berry flux in the brillouin zone is responsible for the intrinsic QAHE. But one of my professors explains the Quantum anomalous hall effect by arguing that the exchange ...
2
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1answer
66 views

axial anomaly for adjoint fermion v.s. fundamental fermion

It is known that the axial anomaly (chiral anomaly, the left L- right R) shows that $U(1)_A$-axial symmetry is not a global symmetry at quantum level. In particular, one can consider the (1) ...
2
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1answer
167 views

Old-fashioned approach to neutral pion’s decay rate

I am uncomfy with the calculation of the neutral pion’s decay rate via the triangle anomaly diagram, which gets touted as evidence of three colors. The calculation invokes PCAC in the guise of the ...
2
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2answers
64 views

In what sense are quasiholes and quasiparticles “excitations” in Fractional Quantum Hall (FQH) systems?

In the theory of Fractional Quantum Hall states, one often sees quasi-holes and quasi-electrons (or quasi-particles) being called "excitations" from the ground state initially given by Laughlin (...
9
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1answer
190 views

How do anomalies work in the causal formulation of QFT?

In the Epstein-Glaser formulation of a QFT, the would-be divergences are taken care of by meticulously splitting the distributions that appear in the construction of the $S$-matrix (or correlation ...
2
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1answer
140 views

Why are critical dimensions and central charge linkable?

From wikipedia: "In order for a string theory to be consistent, the worldsheet theory must be conformally invariant. The obstruction to conformal symmetry is known as the Weyl anomaly and is ...
5
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1answer
127 views

Anomalies and short-distance divergences$.$

Let $J$ be a certain Noether current $$ J=J[\phi] $$ where $\phi$ is a field. This object is classically conserved, although in the quantum-mechanical case it may be anomalous. In the functional ...
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0answers
172 views

Anomalous Ward Identities and anomalous dimensions

Let us consider an action $S[\phi,\partial\phi]$ which is classically invariant under a transformation group $G$. The associated Noether current $\mathcal{J}^\mu$ is classically conserved, namely $\...
2
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1answer
149 views

Why must the conformal anomaly on string worldsheet be cancelled?

Viewing the coordinates of spacetime as fields on string worldsheet, the strings are described by the Polyakov action which presents conformal symmetry (including others) at the claasical level. Now ...
3
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1answer
225 views

How to calculate an axial anomaly in 1+1 dimensions?

As far as I understand, an axial $U(1)$ transformation transforms a two-component spinor like $$ \psi \to \psi'=\text e^{\text i\epsilon \gamma^5 }\psi,\qquad \psi=\begin{pmatrix}\psi_1\\\psi_2\end{...
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0answers
66 views

Anomalous triangle vertex: divergencies and symmetry argument

Consider triangle correlator of one axial-vector current $J_{\lambda 5}$ and two vector currents $J_{\mu}, J_{\nu}$ in a theory with a fermion with mass $m$: $$ \Gamma_{\lambda \mu\nu}(q,p,k) = F\bigg[...
3
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1answer
89 views

Hermiticity of Dirac Operator $\gamma^{\mu}D_{\mu}$ and Expansion in eigenmodes

I'm interested to know under what conditions $\gamma^{\mu}D_{\mu}$ is a hermitian operator. I am studying the Fujikawa method of anomalies and I see that many sources have different answers for this. ...
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2answers
155 views

Conformal theory with zero central charge

Suppose there is a conformal field theory which has the global conformal symmetry namely $SL(2,R).$ and after central extension it is enhanced to Virasoro algebra with central charge, $c=0$ (also ...
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1answer
152 views

Identically vanishing trace of $T^{\mu\nu}$ and trace anomaly

Let us consider a theory defined by an action on a flat space $S[\phi]$ where $\phi$ denotes collectively the fields of the theory. We will study the theory on a general background $g_{\mu\nu}$ and ...
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3answers
640 views

Why are topological properties described by surface terms?

An example are the anomalies in abelian and non-abelian gauge quantum field theories. For example, the abelian anomaly is $\tilde {F}_{\mu\nu}F^{\mu\nu}$ and the integral over this quantity is a ...
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61 views

What is so complex in Hall effect?

I read that Zohar Ringel and Dmitry Kovrizhi of the University of Oxford have proven that creating a computer simulation of one of Earth's phenomena is currently impossible. Technology is not able to ...
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72 views

Can the 't Hooft anomaly of continuous symmetry restrict the spectrum to be gapless?

Let us consider a gapless system $X$ with a global continuous symmetry $G$ only, and no discrete symmetry. In addition, this system has $G$-'t Hooft anomaly, namely that $X/G$ is anomalous. I wonder ...
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1answer
112 views

How to derive an $E_8$ algebra?

What is the simplest way to derive an $E_8$ algebra? I am not interested in $E_8$ itself but what would compel one to think about it. I know for example why you would want to think about $SU(2)$ and ...
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1answer
110 views

Are anomalies a failure of the canonical quantization prescription? Why not?

I would like to understand anomalies from the point of view of the canonical quantization. Noether's theorem claims that, given a continuous symmetry of the Lagrangian, there exists a function Q in ...
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1answer
74 views

Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit?

Quantum Anomalies: Is there a way to show that we recover a classical symmetry that does not exist quantum mechanical in the classical limit? From undergraduate quantum mechanics, I know that we ...
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1answer
156 views

Is it the chiral anomaly which is solely responsible for having instanton effects (and therefore, the $\theta-$term) in the QCD action?

$\textbf{Fact 1}$ In principle, the QCD Lagrangian should contain a Lorentz invariant, gauge invariant, dimension-4 term $\sim\theta \text{Tr}[F^{\mu\nu}\tilde{F}_{\mu\nu}]$. This term, however, is ...
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1answer
129 views

Anomalies of QCD

I have come across the following statement: The anomalies of QCD cannot be reproduced by a collection of free fermions carrying $U(1)_V$, $SU(N_f)_L$ and $SU(N_f)_R$ quantum numbers. That is why ...
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200 views

Can a theory gain symmetries through quantum corrections?

It is well known that not all symmetries are preserved when quantising a theory, as evinced by renormalising composite operators or by other means, which show that quantum corrections may alter a ...
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1answer
257 views

Axial anomaly in QCD VS axial anomaly in current algebra QCD

I would like to understand the distinction between an axial anomaly in QCD (Theta Vacuum: axion -> 2 gluons) and an axial anomaly in QCD of current (Chern–Simons term: pion->two photons, photon->three ...
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1answer
138 views

Possible typo in Schwartz's QFT, p. 629

I'm trying to see whether this is my own misunderstanding or a typo in Schwartz's QFT book. Any help or feedback appreciated. Schwartz talks about Chiral anomalies from the integral measure. The ...