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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46 views

$U(1)^{3} $ anomaly, trace of a hypercharge?

I have recently found the definition of the $U(1)^{3}$ anomaly as: $$\mathcal{A} = Tr[Y^{3}]_{L} -Tr[Y^{3}]_{R} $$ Where $Y$ is the hypercharge of the left, $L$ or right, $R$ components. What I don't ...
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51 views

Is Weyl transformation part of diffeomorphism? Does a gravitational anomaly capture also the anomaly due to Weyl transformation? [duplicate]

Weyl transformation is a local rescaling of the metric tensor $$ g_{ab}\rightarrow e^{-2\omega(x)}g_{ab} $$ Diffeomorphism maps to a theory under arbitrary differentiable coordinate transformations (...
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91 views

$U(1)_A$ effects on the baryons?

We know that the axial $U(1)_A$ is anomalous thus not a global symmetry. Therefore there is no direct associated pseudo goldstone boson for $U(1)_A$. This makes the $\eta'$ much more massive than the ...
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114 views

A critical step in Fujikawa's proof of the Atiyah Singer index theorem

If the Riemannian curvature is zero and $\mathrm{dim}(M)=n=2k$, the Atiyah-Singer index theorem for the twisted Dirac operator reduces to the following equation: \begin{equation}\tag{1} \mathrm{ind}(...
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’t Hooft anomaly matching and massless baryons

In Lectures on Gauge Theory by David Tong there is statement (section 5.6.3 The Vafa-Witten-Weingarten Theorems), that: To invoke the full power of ’t Hooft anomaly matching, we needed to assume that ...
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131 views

With a local anomaly, is the determinant of the Dirac operator still a section of a complex line bundle?

In the literature about anomalies in quantum field theory, the determinant of the Dirac operator plays an important role. The Dirac operator may depend on some background data, and the subject of ...
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88 views

Critical dimension of ${\cal N}=2$ strings

In "A tour through ${\cal N}=2$ strings" by Neil Marcus (https://arxiv.org/abs/hep-th/9211059) the following problem - among others - is noted: The critical dimension of the ${\cal N}=2$ ...
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147 views

Why are gauge anomalies characterised by the non-triviality of $\pi_5(\mathcal G)$?

The folklore in 4-dimensional gauge theories is that the existence of potential gauge anomalies from the triangle diagrams that need to be cancelled are characterised by the non-triviality of the ...
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186 views

Anomaly, symmetries, and Ward identity

I'm trying to bring together and understand the concepts of anomaly, quantum symmetries, and Ward (or Ward-Takahashi, or Slavnov-Taylor) identity in QFT. I think I know what the ideas mean, but I'm ...
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76 views

Can a QFT be anomaly-free on spacetimes that are boundaries but still have an anomaly on other spacetimes?

If $D$ is the Dirac operator for some dynamic spinor fields in background gauge and gravitational fields, then the partition function is supposed to be $\mathrm{det}(D)$. For this to make sense, we ...
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Explanation of $\sum_n\langle\psi_n(x)|(O\psi_n)(x)\rangle=:(\mathrm{tr}\,O)(x)=\mathrm{tr}\int\frac{\mathrm{d}k}{(2\pi)^4}e^{ikx}Oe^{-ikx}$

Let $D$ be the Dirac operator, $O_N:=e^{-(D/N)^2}$ for $N\in\mathbf{N}$ and $\{\psi_n\}$ a complete set of eigenfunctions of $D$. On page $69$ and $78$ of Path Integrals and Quantum Anomalies and in ...
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Anomalies in QFT: why do we require smooth dependence on the background fields?

If $D$ is the Dirac operator for some dynamic spinor fields in a background gauge field $A$, then the partition function is supposed to be $\mathrm{det}(D)$. But if the coupling to the gauge field is ...
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122 views

Reference request - derivation of $\mathrm{ind}\,D_+=-\frac{1}{8\pi^2}\int\text{tr}\,F\wedge F$

Let $D$ be the Dirac operator. The equation \begin{equation}\tag{1} \mathrm{ind}\,D_+=-\frac{1}{8\pi^2}\int_M\text{tr}\,F^2=-\frac{1}{8\pi^2}\int_MF^a\wedge F^b\ \mathrm{tr}(T_aT_b) \end{equation} is ...
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The sign of axion $F$ $F$ dual term in Weinberg

Related to the earlier question $\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki. The sign of axion $F$ $F$ dual term in Weinberg (23.6.16) appears to ...
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82 views

$\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki

The theta angle due to the chiral gamma^5 rotation of chiral fermion results in the phase alpha(x) that has different + or - sign for (1) Peskin&Schroeder, (2) Weinberg or (3) Srednicki. Here ...
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What intuition led to J. Wang and X.G. Wen's lattice formulation of the 3450 chiral gauge theory?

In the paper cited below, Juven Wang and Xiao-Gang Wen give an example of a lattice model that reduces to a chiral $U(1)$ gauge theory at low energy. The low energy theory is called the $3450$ model. ...
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Holomorphic instantons in target torus

For computing instantons contributions from worldsheet torus to target torus, one can evaluate zero modes contribution of genus 1 partition function given by following expression: $$Tr(-1)^FF_LF_Rq^{...
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194 views

Inconsistency in the normal ordered Virasoro algebra

I seem to have found a basic contradiction when it comes to the commutation relations of the Virasoro algebra with normal ordered operators and I am not sure what the resolution is. If we have a ...
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150 views

Holomorphic anomaly at genus 1

Partition function on torus can be defined using a generalized Witten like index as given below: $$F_1=\int_\mathbb{T}\frac{d^2\tau}{\tau_2} Tr(-1)^F F_LF_R \;q^{L_0} \bar{q}^{\bar{L_0}},$$ where $\...
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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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60 views

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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58 views

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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74 views

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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91 views

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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113 views

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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187 views

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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80 views

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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119 views

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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109 views

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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85 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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89 views

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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66 views

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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89 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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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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300 views

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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163 views

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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127 views

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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269 views

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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133 views

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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408 views

'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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