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.
134
questions with no upvoted or accepted answers
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214
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 ...
8
votes
1
answer
498
views
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 $...
- 2,903
7
votes
0
answers
414
views
'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 $Z[A]$), ...
- 814
7
votes
0
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600
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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 ...
- 4,559
7
votes
0
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318
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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 ...
- 1,465
6
votes
0
answers
254
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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. ...
- 54.1k
6
votes
0
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297
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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^{...
- 662
6
votes
0
answers
184
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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....
- 61
6
votes
0
answers
345
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 ...
- 3,504
6
votes
0
answers
386
views
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 ...
- 1,722
6
votes
0
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840
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What is the reason for chiral anomalies in condensed matter systems?
If you consider a massless relativistic fermion theory and you perform a chiral transformation, then you realize that while the classical action remains invariant under this transformation the ...
- 61
6
votes
0
answers
355
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Conformal anomaly of free scalar in 2D
I'm trying to calculate the conformal anomaly $c$ of a free scalar on a 2-sphere. I've seen other, indirect ways to do this, but since this is a free theory I feel like it should be possible to see ...
- 913
6
votes
1
answer
814
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String theory and trace anomaly in semiclassical gravity?
what does string theory have to say about the trace anomaly in the expectation value of the stress-energy tensor of massless quantum fields on a curved background and its interpretation as the ...
- 648
5
votes
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answers
166
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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 , \...
- 141
5
votes
0
answers
105
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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 ...
- 8,460
5
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145
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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},...
- 1,465
5
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answers
204
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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 ...
- 51
5
votes
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answers
231
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Where does chiral matter at conical singularities "come from" in M-theory?
It seems to be accepted that to produce chiral fermionic matter in a compactification $\mathbb{R}^4\times X$ of M-theory/11d SUGRA to four dimensions, we need the seven-manifold $X$ to have isolated (...
- 125k
4
votes
0
answers
125
views
Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$1+2+3+...=-1/12$$ to find the zero point energy of the bosonic string (and later used the result to argue that we must have ...
- 1,686
4
votes
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154
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Why does Tong uses Euclidean Gamma matrices in this step of deriving the Chiral Anomaly?
In David Tong's GT notes on page 137, he uses the trace identity for Euclidean gamma matrices given by
$$\text{Tr}(\gamma^5\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma})=4\epsilon^{\mu\nu\rho\...
- 113
4
votes
0
answers
181
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Stress tensor trace anomaly in two dimensions
I'm trying to calculate the expectation value of the stress tensor in 2D following the book "Quantum fields in curved space" (Birrell and Davies). In 2D the divergent contribution to the one-...
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4
votes
0
answers
189
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Why 't Hooft anomaly can be described by some characteristic class?
In some recent papers, such as Zohar PhysRevB.97.054418, Zohar arXiv:1705.04786, Metlitski PhysRevB.98.085140, the authors state that the anomaly inflow term/ topological action can be expressed in ...
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4
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232
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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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4
votes
0
answers
89
views
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 ...
- 3,504
4
votes
1
answer
881
views
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{...
- 4,689
4
votes
0
answers
291
views
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 ...
- 251
4
votes
0
answers
213
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How can we find the consistent form of the anomaly from the Fujikawa method?
The Fujikawa method to find the chiral anomaly allows us to find for the axial current
$$\partial_\mu j^\mu=-\frac{g^2}{16\pi^2}\epsilon^{\mu\nu\rho\sigma} Tr F_{\mu\nu}F_{\rho\sigma},$$
which is the ...
- 451
4
votes
0
answers
129
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The chemical potential as the zeroth component of a constant gauge field
The chemical potential $\mu$, is introduced in the action as the lagrange multiplier
$$
\tag 1 S[Q_{0}] \to S[\mu] = S[Q_{0}]-\int dt \mu Q_{0}(t),
$$
where
$$
Q_{0}(t) = \int d^{3}\mathbf r J_{0}(\...
- 8,821
4
votes
0
answers
110
views
Inconsistency in regularization with parallel and perpendicular momenta
In deriving the axial anomaly Peskin and Schroeder use dimensional regularization, continuing loop momenta to $ 4 - \epsilon $ dimenstions. The loop momenta can now be split into pieces ``parallel'' ...
- 8,994
4
votes
0
answers
648
views
Effective field theories and gauge anomalies cancellation
Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
- 8,821
4
votes
0
answers
488
views
Anomaly for Majorana fermion?
In 4-spacetime dimension, is there U(1) gauge field chiral anomaly associated with Majorana fermion (or I am not sure if it is equivalent, majorana representation)? Besides, I have read from several ...
- 421
3
votes
0
answers
65
views
Relation between the Casimir energy and the central charge in CFT in general
In 2d CFT we know that the Casimir energy of the vacuum is proportional to the conformal central charge $c$.
$$
F_L=f_0 L-\frac{\pi c}{6 L} \tag{1}
$$
where $F$ is the free energy and L is the ...
- 31
3
votes
0
answers
67
views
Questions about the treatment of anomalies
I was reading Schwartz's QFT book, and in Chapter 30, he introduces the calculations of anomalies by evaluating objects like $\partial_\mu\langle J^{\mu 5}J^\nu J^\alpha\rangle$, where $J^5$ is ...
- 324
3
votes
0
answers
166
views
Witten anomaly and bound states of fermions
In his famous paper "An SU(2) anomaly", Witten begins by noting that an SU(2) gauge theory with a single fermion in the doublet representation is weird, since there is "no obvious ...
3
votes
0
answers
66
views
Restoration of symmetry explicitly broken by anomaly
What is the meaning of the restoration at finite temperature of a symmetry that is "broken" by the presence of an anomaly. If the symmetry is not there why is it restored at finite ...
- 841
3
votes
0
answers
62
views
Why do the two Euclidean Dirac 'measure's change via the same rule under local chiral transformations?
I am reading Weinberg QFT vol 2 p.362~370, which is on calculating the Abelain anomaly.
On p.369, the book says the two Dirac spinors $\psi$ and $\overline{\psi}$ are entirely independent in the ...
- 1,431
3
votes
0
answers
107
views
Why are there only two 496-dim. gauge groups $E_8\times E_8$ and $SO(32)$ allowed in string theory? Why not $E_8\times U(1)^{248}$ or $U(1)^{496}$?
While constructing anomaly-free string theories with $\mathcal N=1$ supersymmetry (16 supercharges constituting a Majorana-Weyl spinor), we learn that the gauge group must be 496-dimensional in order ...
- 71
3
votes
0
answers
87
views
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 ...
- 4,306
3
votes
1
answer
122
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 ...
- 857
3
votes
0
answers
261
views
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(\...
- 41
3
votes
0
answers
338
views
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.
$$
\ln \frac{ Z[\delta+h] }{Z[\delta]} \approx\, \frac{1}{8\pi^2}\...
- 3,098
3
votes
0
answers
147
views
Principal bundles of Lie groups in a short exact sequence
Consider a short exact sequence of Lie groups
$$1 \rightarrow G \rightarrow H \rightarrow L \rightarrow 1.$$
What can we say about the principal bundles with the above groups as structure groups (...
- 329
3
votes
0
answers
111
views
Gauge anomaly from conformal dimension?
According to ref.1, the Chern-Simons theory $\mathrm{SU}(N)_k$ has a $\mathbb Z_N$ one-form symmetry with anomaly
$$
\eta=\exp\left[-2\pi i \frac{k}{N}\right]\tag{4.12}
$$
which, apparently, can be ...
3
votes
0
answers
238
views
Energy-Momentum Tensor and Variation of the Partition Function
I am currently working through the Fujikawa paper "Comments on Chiral and Conformal Anomalies". I have, however, had some issues getting around some notation, and perhaps a little of the logic, he ...
3
votes
0
answers
192
views
Gravitational anomaly: When these occur?
Consider the partition function for a quantum-gravitational theory
$$Z=\int D[\Xi]e^{iS(\Xi)}$$
Here, $\Xi$ is a configuration variables for space time; this variable must not necessarily be the ...
- 3,428
3
votes
0
answers
175
views
Interpretation of the chiral anomaly a-la Alvarez-Gaume
In the paper "The topological meaning of non-abelian anomalies" written by Alvares-Gaume and Ginsparg they argue the appearing of the (gauge) anomaly in a theory with chiral fermions in the following ...
- 8,821
3
votes
0
answers
98
views
Effective field theory with coordinate dependent "axion"
Suppose the theory of fermions interacting with EM field and the axial 4-vector $b_{\mu}$:
$$
S = \int d^{4}x \bar{\psi}\gamma^{\mu}(i\partial_{\mu} + eA_{\mu} +\gamma_{5}b_{\mu})\psi
$$
We want to ...
- 8,821
3
votes
0
answers
234
views
Consequences of anomalies
I'm trying to understand the phenomenological consequences of an anomalous global symmetry. In 't Hooft's "Symmetry breaking through Bell-Jackiw anomalies", he states in the abstract:
In models of ...
- 31
3
votes
0
answers
466
views
Fujikawa's method for 2+1-dimensional parity anomaly?
Fujikawa's chiral rotation method is applied to calculate 3+1 dimensional chiral anomaly in many textbooks, but is there any counterpart of that method in deriving 2+1 dimensional parity anomaly, i.e. ...
- 421
3
votes
0
answers
855
views
Chiral Anomaly in Massless QED
Classical massless QED has axial current conservation. When quantizing the theory, we expect that suddenly $\partial_\mu \hat{j}^{\mu5}\neq0$ (as an operator equality).
I have two questions regarding ...
- 2,004