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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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Does the vanishing of the one loop beta function imply no running to all orders?

This question sounds ridiculous, but bear with me. I am having a hard time reconciling the following two facts: Classical global symmetries can become anomalous upon quantization, and the anomalous ...
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1answer
53 views

Viewing anomalous dimensions in RG as a quantum anomaly

Other than sharing the word “anomalous”, both the anomalous dimension in RG and the more well-known quantum anomalies (such as chiral anomaly) share a common feature. These are violations of classical ...
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1answer
38 views

In the case of the Dirac Equation,what forbids the free electron to absorb a photon? (electron magnetic moment)

It is straightforward to show from relativistic kinematics that a free electron cannot absorb a photon, as shown in this previous thread. However, It is also known that using the Dirac equation, you ...
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2answers
172 views

Weyl anomaly in 2d CFT (string theory lectures by D.Tong)

In his lectures on String Theory (http://www.damtp.cam.ac.uk/user/tong/string.html), Tong gives a proof of the Weyl anomaly, using equation $(4.36)$. It seems wrong to me. Here he uses the OPE ...
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Anomaly is due to the noninvariance of the path-integral under a symmetry. Is the noninvariance reflected on 1PI effective action?

When a symmetry is anomalous, the path integral $Z=\int\mathcal{D}\phi e^{iS[\phi]}$ is not invariant under that group of symmetry transformations $G$. This is because though the classical action $S[\...
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1answer
64 views

Nielsen-Ninomiya Theorem versus Chiral Gauge Anomaly

As far as I understand, the Nielsen-Ninomiya theorem states that (under mild conditions) the number of left and right-handed chiral fermions must be equal on the lattice, while the chiral gauge ...
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71 views

Parity Anomaly and Gauge Invariance

In Fermionic Path Integral and Topological Phases, Witten shows that in $2+1$ dimensions, the free massless Dirac fermion suffers from parity anomaly. To be specific, he shows that it is impossible to ...
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59 views

Why Parity Anomaly in Odd Dimensions?

In section 13.6 of Nakahara, the parity anomaly is in odd dimensional spacetime. From the paper Fermionic Path Integral And Topological Phases by Witten, the problem appears as one cannot define the ...
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1answer
115 views

When is an anomaly one-loop exact?

There are many examples of quantum anomalies that are one-loop exact, and many examples of anomalies that have contributions to all orders in perturbation theory. I haven't been able to identify a ...
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1answer
85 views

APS $\eta$-invariant and spin-Ising TQFT

I am interested in the relation between the Atiyah-Patodi-Singer-$\eta$ invariant and spin topological quantum field theory. In the paper Gapped Boundary Phases of Topological Insulators via Weak ...
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1answer
46 views

How does the global $G^2G'$ anomaly make all the $\theta$-vacua associated to the gauge group $G$ physically equivalent?

Consider a gauge group $G$ and suppose that there is a $\theta$-term associated to it. According to this answer, the existence of a global anomalous symmetry $G'$ which rotates the $\theta$-term, ...
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1answer
69 views

What does $B+L$ anomaly have to do with a phase redefinition of the left-handed quark field?

According to this answer, the reason why $SU(2)_L$ weak theory does not have a theta vacuum is because any theta term can be reabsorbed with a phase redefinition of the left-handed quark field. ...
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1answer
84 views

“The operators with nontrivial vacuum expectation values have to soak up the zero modes associated to the anomaly.”

I was reading ref.1, where one can read (emphasis mine) ... the vacuum expectation value $\langle \mathcal O_{\phi_1}\cdots \mathcal O_{\phi_\ell}\rangle$ vanishes unless $$ \sum_{k=1}^\ell\...
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1answer
123 views

What is the physical interpretation of chirality / chiral anomaly?

I'm dealing with this paper from C. Bär and A. Strohmeier about a rigorous derivation of the chiral anomaly. I'm not quite familiar with the physical context of chirality and its anomaly. What ...
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1answer
94 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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120 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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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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0answers
35 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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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 ...
3
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1answer
74 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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79 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
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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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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
80 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
111 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
72 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
53 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 ...
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1answer
78 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 ...
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50 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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72 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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32 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
91 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
47 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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83 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
127 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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125 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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192 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
95 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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31 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 ...
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1answer
89 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) ...
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1answer
193 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 ...
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2answers
72 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 (...
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1answer
194 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 ...
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1answer
167 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 ...
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1answer
133 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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220 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
188 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 ...
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1answer
272 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
73 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[...