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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59 views

't Hooft anomaly implies spontaneous symmetry breaking?

It isn't clear to me why an 't Hooft anomaly implies spontaneous symmetry breaking. I would like to see an argument which shows this. The most I can say about this scenario is that if the symmetry ...
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Symmetries in quantum field theory and anomalies

Suppose we have a lagrangian quantum field theory, thus a theory where we can write an action in the form \begin{equation} S = \displaystyle \int d^4 x \; \mathcal L \, \left( \partial_{\mu} \phi , \...
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Calculating traces for triangle diagrams with massless fermions

I am following Schwarz Quantum Field Theory textbook. In particular, I am looking at triangle diagrams with massless fermions. On pg. 623 - 624 Schwarz attempts to calculate $q_\mu^1 M_{5}^{\alpha\mu\...
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Axial anomaly at the level of particles

Consider pure QED with massless electrons. Due to the axial anomaly the axial current is not conserved: $$ \tag 1 \partial_{\mu}J^{\mu}_{5} \sim F_{\mu\nu}\tilde{F}^{\mu\nu} $$ On the other hand, it ...
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Symmetry anomaly and energy spectrum

Let us consider 't Hooft anomaly: \begin{eqnarray} Z[A^\lambda]=Z[A]\exp(i\alpha[A,\lambda]), \end{eqnarray} where $A$ is the background $G$-gauge field and $\lambda$ is some $G$-gauge ...
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1answer
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Fujikawa Jacobian for Baryon number anomaly

Reviewing the anomalies of the standard model, one knows that the Baryon number is not conserved because of an anomaly associated to the global $U(1)$ symmetry that quarks have. That is the current $$...
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1answer
55 views

What's the difference and connection between symmetry breaking and anomaly?

I'm just wondering what's the difference between symmetry breaking and anomaly. From my understanding, symmetry breaking means: there is a symmetry in the action, but in the ground state of the ...
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Chiral anomaly in Weyl semimental

In Weyl semimetal, there is an analog of ABJ anomaly, which is a $E \cdot B$ term. The ABJ anomaly can be viewed as winding number because of the homotopy group of sphere $\pi_3(S^3)= \mathbb{Z}$ for ...
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Chiral anomaly for massless Dirac fermion

Let us assume we have a single flavor massless Dirac fermion with Lagrangian $\mathcal{L} = \bar{\psi}i\gamma^{\mu}D_{\mu}\psi + \mathcal{L}_{gauge}.~$ Due to chiral anomaly, chiral symmetry is not a ...
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Gauge invariance of the regulator when calculating the chiral (ABJ) anomaly by the Fujikawa method

I am currently studying the calculation of chiral anomaly using fermionic path integral. In all texts I looked at, the authors simply use a regulator of the following form $e^{(\gamma_{\mu}D^{\mu})^...
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Low energy description of Symmetry Enriched Topological phases

Prelude: low energy description of Symmetry Protected Topological (SPT) phases It is known [1] that the low energy effective description of SPT phases, protected by a group $G$ is an invertible ...
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Among free quantum field theories, do all 't Hooft anomalies arise from chiral fermions?

In quantum field theory, a global symmetry group that can't be gauged is said to have an 't Hooft anomaly. One of the most familiar examples is the free massless Dirac fermion in $3+1$ dimensional ...
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Can Lorentz/Poincare symmetry be anomalous?

The question is in the title. Can a Poincare invariant Lagrangian lead to a path integral that is not Lorentz or Poincare invariant? If so, can I have an example? A related confusion: on page 426 of ...
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Why do we solve the Wess-Zumino consistency condition using the method of descent?

Consider a quantum field theory in $d$ dimensions with a symmetry $G$. For the purpose of this discussion let's say that $d$ is even and $G$ is a compact, connected Lie group. We say that the symmetry ...
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2answers
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Are there versions of String Theory formulated in $D$ spacetime dimensions or even in infinitely many dimensions?

There are a lot of different versions of string theory, and almost all of them differ in the number of dimensions. The most famous ones are formulated in 10, 11 or 26 dimensions. But are there any ...
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't Hooft vs ABJ anomalies [closed]

At some point in our physics education, we begin to accumulate a bunch of slogans related to anomalies. At some (later, in my case) point, we learn that actually there were two different kinds of ...
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Integral in direct calculation of anomalies

I am trying to follow Weinberg's triangle diagram calculations in section 22.3 of volume II of The Quantum Theory of Fields. He reduces the calculation to evaluating the integral \begin{equation} \...
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1answer
80 views

Chiral anomaly: UV or IR effect

In TASI 2003 Lectures on Anomalies (section 1.6) Jeffrey A. Harvey present arguments, why chiral anomaly is IR effect (in contrast to calculation, where UV regulator was used): Only massless ...
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Anomaly inflow mechanism

I know very simple example of anomaly inflow. See section 4.4 in David Tong: Lectures on Gauge Theory. As I read, such mechanism have some applications in condensed matter and in quantum field theory, ...
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1answer
90 views

Anomalies on boundary and bulk physics

Few times I faced with such statements: The gravitational anomaly of the 1+1d boundary system is known to be proportional to the thermal Hall conductivity of the 2+1 dimensional bulk How ...
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't Hooft Anomaly Equivalent Definitions

I've seen a 't Hooft anomaly defined in two ways. Roughly, a theory has a 't Hooft anomaly when Once the theory is coupled to a background gauge field $A$ (so study eg the partition function $Z[A]$), ...
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Polchinski Weyl Anomaly from perturbing the flat background. Eq (3.4.22)

In deriving the Weyl anomaly for the bosonic string using a perturbation around a flat background, Polchinksi uses Eq. (3.4.22), i.e. $$ \ln \frac{ Z[\delta+h] }{Z[\delta]} \approx\, \frac{1}{8\pi^2}\...
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Classification of higher Symmetry Protected Topological (SPT) phases

Suppose that we have a $d$ dimensional bosonic SPT phase, protected by some $p$-form symmetry, $G^{[p]}$. Suppose also that it is classified within group cohomology, so that we don't have to run into ...
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Loop counting for determinants and anomalies

I am trying to understand an argument for why anomalies are one-loop exact, given by Bilal in Lectures on Anomalies. The relevant paragraph is reproduced here: Let us first explain why the anomaly ...
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Why the contact terms in the Ward identity vanish due to the invariant Noether currents?

The picture below is a screenshot of Srednicki's QFT textbook. ------------------------------ ------------------------------ $j^{\mu}$ is the current associated with the $U(1)$ gauge symmetry; $...
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Chiral anomalies and triangle diagrams

In the computation of the Adam-Bell-Jackiw anomaly, in Peskin and Schroeder's book they proceed with a regularization of $\partial_\mu j^{\mu 5}$ by evaluating the fields at different spacetime points ...
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Anomalies in QFT

I am a first year PhD student in theoretical physics with a background in QFT (up until relativistic fields, path integrals and gauge theories and anomalies) and some algebraic topology but my ...
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Why do we think that the $U(1)$ problem is solved by instantons?

It is usually thought that the $U(1)$ problem is solved when 't Hooft realized that instantons induce additional symmetry breaking of the $U(1)_A$ symmetry aside from the non-vanishing quark masses. ...
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Gravitational correction in index theorem for 3+1 time-reversal invariant TI

In Witten's review paper: Fermion path integrals and topological phases, the index theorem for 3+1 $\mathcal{T}$-conserving TI is given by $$e^{\mp i\pi \eta/2}e^{\pm i\pi(P-\hat{A}(R))}=(-1)^{\...
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129 views

OPE of stress tensor in CFT

I come aross an OPE between stress tensor components in CFT which is \begin{equation} T(z)\bar{T}(\bar{w})\sim -\frac{\pi c}{12}\partial_{z}\partial_{\bar{w}}\delta^{(2)}(z-w)+... \end{equation} I am ...
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Principal bundles of Lie groups in a short exact sequence

Consider a short exact sequence of Lie groups $$1 \rightarrow G \rightarrow H \rightarrow L \rightarrow 1.$$ What can we say about the principal bundles with the above groups as structure groups (...
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1answer
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Casimir Force and bosonic String Theory dimensions

I was reading the lecture notes on Quantum field theory by David Tong. In the section on Casimir force he derived the force of attraction felt by the plates due to the field vacuum energy in $1+1$ ...
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If a regularization procedure respects a symmetry, is this symmetry unbroken in perturbation theory?

I read in this paper the statement that a proof that SUSY is preserved in perturbation theory would be the existence of a regularization procedure which respects SUSY (for a particular theory). Is ...
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1answer
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About the spontaneous breakdown of an anomalous symmetry

If a global symmetry is anomalous, classically it is still possible to talk about spontaneous breakdown of that symmetry. In particle physics, do we have such an anomalous symmetry (or symmetries) ...
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New symmetries upon quantization

In standard field theory texts, a “classical symmetry” is defined to be a transformation $\phi\to\phi’$ such that the corresponding action is left invariant. The symmetry is said to survive ...
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Standard model extension

this Semester I have my first QFT class and we have a homework where I got stuck at the beginning. I have some ideas but I am not sure if they are correct, so I don't want a solution, I only want to ...
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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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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
90 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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1answer
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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
122 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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1answer
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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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