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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Chiral vortical effect (CVE) and gravitational anomaly

Chiral vortical effect is a generation of an axial current in the presence of the rotation. On the one hand, the expression for the $\mathbf{CVE}$ has the following form: $$ \vec{J}^{5} = \vec \Omega \...
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Anomalies in the self-dual Yang-Mills theory and $\mathcal{N}=2$ open-string theory

I am reading a paper, written by G. Chalmers and W. Siegel - https://arxiv.org/abs/hep-th/9606061, where they discuss the action of self-dual Yang-Mills theory, which in light-cone formalism is ...
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1answer
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Regularization of $\delta$ function and Chiral anomaly in gravity

Mark Srednicki's QFT book presents a regularization of the $\delta$ function in calculating the chiral anomaly (see section 77 of the book). This regularization reads \begin{equation} \delta (x-y)=\...
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Why color anomaly is in the axion photon coupling?

The axion photon coupling is given by the expression $ g_{a\gamma\gamma}= \frac{\alpha}{2\pi f_a}(\frac{E}{N}-\frac{2}{3}\frac{4m_d+m_u}{m_d+m_u}) $, where $f_a$ PQ symmetry breaking scale, $E$ and $...
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1answer
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Anomalous global symmetry in non-gauge theories

I’m a bit confused on the effects of anomalous global symmetries. So take for instance the following theory $$\mathscr{L}=\partial_\mu\phi\partial^\mu\phi^*+i\bar{\psi}\gamma_\mu\partial^\mu\psi-y \...
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Confusion about chiral anomaly (Fujikawa's method)

I am reading Fujikawa's method for calculating chiral anomaly, see this wiki page. The method can be described as follows. It starts with the path integral \begin{equation} Z=\int\mathcal{D}\psi\...
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1answer
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How do we know there doesn't exist an anomaly that implies that there is no good choice of dimension for the bosonic string?

By considering $\langle T^\alpha_\alpha\rangle$, the Weyl anomaly, we can show that the critical dimension, $D=26$ is the only possible choice of dimension for the bosonic string. However, how do we ...
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Does the Gibbons-Hawking boundary action have an anomaly inflow interpretation?

The Einstein-Hilbert action on a manifold $M$ with boundary is $$\frac{-1}{16\pi G}\int_M d^n x \sqrt{-g} R +\frac{1}{8\pi G} \int_{\partial M} d^{n-1}x \sqrt{|h|} K$$ where $K$ is the extrinsic ...
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1answer
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On-site symmetries can be gauged, but is a gaugeable symmetry necessarily on-site?

I've always liked lattice QFT because it's mathematically unambiguous and non-perturbative, but it does have two drawbacks: (1) the lattice is artificial, and (2) some features are messy. One of those ...
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1answer
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How can we know a gauge theory is not anomalous?

Say we have a putative 4d gauge theory coupled to fermions of various representations. In order for this theory to be consistent, we need to check that no there are both no triangle anomalies and no ...
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Weyl Anomaly Derivation in Polchinski Eq (3.4.21)

In Polchinski's longer derivation of the Weyl anomaly, he arrives at the result (equation 3.4.19): $$ \ln{\frac{Z[g]}{Z[\delta]}} = \frac{a_1}{8\pi} \int d^2\sigma \int d^2\sigma' g^{1/2} R(\sigma) G(\...
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Bosonic SPT phases with time reversal and a $Z_2$ symmetry

Consider a bosonic system with time reversal symmetry $\mathcal{T}$ and a unitary on-site $\mathbb{Z}_2$ symmetry. Suppose the symmetry is realized in a special way such that $$\mathcal{T}^2= (-1)^B$$ ...
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Conformal and chiral anomalies

In presentation On conformal anomalies of some 6d superconformal theories was mentioned that there are some relations between chiral/gravitational and conformal anomalies. For me, it is very ...
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Phenomenology application of quantum anomaly

Anomaly means that: the system has a symmetry at classical level (both discrete and continous), but when we quantize the theory, the system no longer holds the symmetry. I'm wondering for every ...
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How does anomaly inflow work in terms of the eta invariant?

I'm trying to understand the non-perturbative picture of anomaly inflow, mainly following these two articles by Witten and Yonekura: [1] - https://arxiv.org/pdf/1909.08775.pdf , [2] - https://arxiv....
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'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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1answer
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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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1answer
50 views

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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1answer
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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
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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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1answer
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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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1answer
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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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1answer
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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
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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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2answers
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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
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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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1answer
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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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1answer
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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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2answers
550 views

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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1answer
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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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1answer
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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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1answer
107 views

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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