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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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Weinberg Volume II: Abelian Anomaly Function

The following is from page 363 of Weinberg volume II. We wish to evaluate the RHS of \begin{align}\label{EQbbvbv} [d \psi][d \bar{\psi}] \rightarrow(\operatorname{Det} \mathscr{U} \operatorname{Det}...
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Critical dimension from the symmetries of the string action

(Related: This post and this post.) In this thesis it is said (on page 13) that just by assuming that we have some general action with the same symmetries as the Polyakov action (Poincare invariance, ...
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Factor of 2 issue in the non-gauge invariance of Chern-Simons theory with a boundary

It is well known that the Chern-Simons (CS) theory by itself is not gauge invariant in the presence of a spacetime boundary. Concretely, suppose the flat half space $\mathcal{M}$ with $x\in \mathbb{R},...
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Why does calculating $\langle J^{\alpha 5}(x) J^{\mu}(y) J^{\nu}(z)\rangle$ involve certain triangle diagrams?

In deriving the chiral anomaly, one wishes to compute the correlation of the axial-vector-vector currents. One writes this explicitly as $$\int d^4xd^4yd^4z \, e^{-ipx} e^{iq_1y}e^{iq_2z} \langle [ \...
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How to prove that a given correlation function is protected?

I would be interested in proving that $2$-point functions made of $1/2$-BPS operators are protected in $\mathcal{N}=4$ SYM (Supersymmetric Yang-Mills), i.e. that the correlator $\langle \mathcal{O}_2(...
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1answer
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Peskin's treatment of Pions as Goldstone Bosons

After restoring the mass terms in the Lagrangian \begin{align} \mathcal{L}=\bar{u} i \not D u+\bar{d i} \not D d-m_{u} \bar{u} u-m_{d} \bar{d} d, \end{align} one obtains equations of motion for the ...
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Chiral anomaly: gauge covariance and regularization

I am looking at the treatment of the chiral anomaly in Fujikawa and Suzuki's "Path Integrals and Quantum Anomalies." To illustrate the quantum breaking of chiral symmetry (section 4.3), they start ...
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Is there a way to make this simple “derivation” of the Trace Anomaly correct?

I think I came up with a simple yet sketchy almost-proof of the trace anomaly (A.K.A. Weyl anomaly) in 2D CFT, but it has the wrong prefactor. I was wondering if anyone could assess whether this "...
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1answer
58 views

Gauge anomaly in Polyakov string and Faddeev-Popov method

I am currently trying to gain a better understanding of the gauge fixing procedure used in chapter 5 of David Tong's notes. Since the central charge of the Polyakov action for, say, the bosonic ...
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Anomalies depend on how they are calculated. How is this satisfactory?

If we have a set of linear symmetry currents $J^{\mu}_{\alpha}$ and attempt to find if they are anomalous, we find that if we change the regularization procedure, the anomaly will get mixed around the ...
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Intuitive way to get 10 dimensions in string theory?

To get the 26 dimensions is sort of intuitive (in a handwavey sort of way). Basically we solve: $$(D-2)\frac{1}{2}(1+2+3+4+...)=-1$$ Where $1+2+3+..$ times $\frac{1}{2}\hbar$ are the ground energy ...
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Momentum replacement in the axial anomaly calculation in dimensional regularisation (‘t Hooft prescription)

I have been studying the axial anomaly and everywhere I see the calculation of the triangle loop using dimensional regularisation (see for example pages 661-664 of section 19.2 of Peskin). In the ‘t ...
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1answer
61 views

Anomaly vs spontaneous symmetry breaking

I was trying to gain a basic understanding of anomalies. In the case of anomalies, certain correlations which should have been zero based on symmetry considerations of the action, instead turn out to ...
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Time-reversal (explicitly) broken surface of $(3+1)$-dimensional topological insulator

Let us consider the surface of $(3+1)$-dimensional topological insulator, which is protected by the charge conservation $U(1)_Q$ and a time-reversal symmetry $\mathbb{Z}_2^T$. Such a surface, if not ...
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Exotic perturbative anomaly captured only by higher-loop Feynman graphs, but not by any 1-loop Feynman graph?

My question: Are there any perturbative anomaly captured by higher-loop but not by captured at the 1-loop Feynman graph (say, not enough)? We are familiar with the text book example of a ...
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1answer
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Anomalies in Global Symmetries (Srednicki ch 76)

In chapter 76 of Srednicki's QFT book, he defines $C^{\mu\nu\rho}(p,q,r)$ via (76.21) \begin{equation} (2\pi)^{4}\delta^{4}(p+q+r)C^{\mu\nu\rho}(p,q,r)\equiv \int d^{4}xd^{4}yd^{4}z e^{-i(px+qy+rz)}\...
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How is group cohomology in SPT's related to the 't Hooft anomaly on the boundary?

I understand that group cohomology description for symmetry protected topological phases (SPT) comes from discrete nonlinear sigma models. A tutorial on this can be found in the excellent lectures by ...
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Particle on a circle with magnetic flux$.$

I am trying to understand the model studied in 1905.09315 §2, to wit, a $0+1$ dimensional theory with target space $\mathbb S^1$ with non-trivial magnetic flux: $$ \mathcal L=\frac12m\dot q^2-\frac{i}{...
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1answer
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Why does a triangle anomaly appear in a gauge theory?

I have read that when we construct a theory with abelian gauge symmetry there will appear some anomalies when we do the quantum correction to the theory. In 4D space such anomalies are explained by ...
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68 views

Higher point anomalies cancellation from trace

I had asked this question within this one before, but having also made other 2 independent enough questions there, decided to ask this one by itself here. So, it is a well known fact that the ...
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1answer
55 views

Nuclei violating B number

Within SM, it is know that baryon number is not preserved and changes as $$ \Delta B = 3·\Delta n_{CS}, \quad n_{CS} \in \mathbb{Z}\ ({\rm Chern-Simons\ index\ for\ vacuum}) \tag1$$ Then, its ...
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B violation and electric charge

Within SM you can prove that despite we have baryon number conservation respect to Noether theorem, at quantum level baryon (and lepton) number is violated as $$ \Delta B = 3·\Delta n_{CS}, \quad n_{...
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Is string theory self-consistent? (Conformal anomaly)

Recently I attended a very short course on string theory. We went through the standard presentation in light-cone gauge for brevity. We ‘derived’ the Einstein field equation in the following manner. ...
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Diagrammatic expansion of an operator insertion in path integral for Trace Anomaly calculation

Starting with a scale invariant classical field theory, we can prove that the energy-momentum tensor will be traceless. \begin{equation} \Theta^\mu_{\ \mu }=0 \end{equation} In the context of the ...
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Relation between the trace anomaly and the energy-momentum tensor being off-shell

Let's say we have a massless QED theory with a Lagrangian \begin{equation} L=i\bar{\psi}\not{D}\psi-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} \end{equation} The symmetric energy-momentum tensor is \begin{...
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3answers
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What really enforces technical naturalness of electron mass?

Technical or 't Hooft naturalness A parameter $\theta$ in the Lagrangian of a field theory is said to be natural, if in the limit of vanishing $\theta$, the theory has some enhanced symmetry. If this ...
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Ward identity for 'general' operator and current diagrams

This is actually about two related doubts and I hope is appropriate for a single question (if not, I will happily divide it). So, my problems are related to the analysis and calculation of chiral ...
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83 views

Peskin equation on the treatment of chiral anomaly

In page 666 (it couldn't be other way - bad joke), chapter 19, the Eq. (19.73) claims (see properties of the $\phi_n(x)$ functions in this post: Change of variables in path integral measure): $$ \...
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References to understand BRST Quantization

I'm looking for good, rigorous references that discuss BRST quantization in relation to how it leads to dealing with anomalies and ghost fields. I'm looking at high level references (i.e., assume ...
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QCD Trace Anomaly and Mass

In the paper in equations 4 and 5, some of the mass of the nucleons comes from the "trace anomaly" of the QCD energy-momentum tensor (as described in the paragraph following these equations). Is there ...
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2answers
280 views

How do anomalies affect the field equations of motion?

I find anomalies an extremely unintuitive subject, because they're studied so indirectly. In the standard textbook presentation, one computes an abstract quantity that should be zero classically (say, ...
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How does the Weyl anomaly imply $\langle T^{\mu}_{\mu} \rangle \neq 0$?

I want to consider the case of euclidean field theory in 2 dimensions with the action $$S[\phi]=\int \! d^2\!x \sqrt{\det(g)}g^{\mu\nu}\partial_\mu\phi\partial_\nu\phi$$ which leads to a partition ...
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1answer
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Does the massless fermion in $2+1$ dimensions suffer from gauge anomaly?

In Fermion Path Integrals And Topological Phases Witten showed that for a massless Dirac fermion in $2+1$ dimensions $$S[\bar{\psi},\psi]=\int d^{3}x\bar{\psi}iD\!\!\!\!/_{A}\psi,$$ where $A$ is a $...
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1answer
104 views

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
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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
47 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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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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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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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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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
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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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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
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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
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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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“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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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
118 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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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'...