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.
363
questions
4
votes
0
answers
89
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 ...
- 1,628
1
vote
0
answers
59
views
Possible bound state for fermion doublet vis-a-vis the Witten anomaly
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 ...
1
vote
0
answers
72
views
Anomalies, 2-cocycles and (D+1)-cocycles
I'm learning about anomalies and I'm a bit confused about their relationships to 2-cocycles and 3-cocycles (in the group cohomology $H^{\bullet}(G, U(1))$). The below might only apply to 't Hooft ...
- 123
2
votes
0
answers
38
views
$U(1)_A$ axial anomaly for $SU(N)$ gauge theory in 1+1 dimensions
In massless Abelian gauge theory in 1+1 dimensions, the divergence of axial current is given by
\begin{align*}
\partial_\mu j_A^\mu=\frac{e}{2\pi}\epsilon^{\mu\nu}F_{\mu\nu}=\frac{e}{\pi}F_{01}.
\end{...
- 105
2
votes
0
answers
48
views
Vanishing Chern-Simons partition function
I was reading again the article "Generalized Global Symmetries" and I notice that in the beginning of page 22, they argue that after gauging the $\mathbb{Z}_k$ one-form symmetry, of Chern-...
- 311
0
votes
0
answers
24
views
Prerequisites and Resource recommendations for Quantum Anomalies [duplicate]
I am going to start reading about Quantum Anomalies. I have done quantum field theory but have not understood renormalization well. Is renormalization something that is needed for studying Quantum ...
1
vote
0
answers
62
views
Anomalous magnetic dipole moment of muon
I'm currently studying for my oral exams and came across exercise 17.1 in Schwartz's Introduction to Quantum Field Theory. In the exercise, we consider the following Lagrangian for super symmetry:
$$\...
- 135
0
votes
0
answers
23
views
Gauge anomalies vs. non-gauge bosons
When computing gauge anomalies, besides transformations under gauge groups, local Lorentz transformations are considered for (mixed) gravitational anomalies. It leads to inclusion of gravitons among ...
- 77
2
votes
1
answer
71
views
Light-cone quantization of open string as derived in Polchinski
Polchinski uses the following gauge conditions, but I don't follow this procedure of gauge fixing and quantization:
\begin{align}
X^+ = \tau, \tag{1.3.8a} \\
\partial_\sigma \gamma_{\sigma \sigma} = 0,...
- 413
0
votes
0
answers
29
views
Why M-theory has eleven dimensions? [duplicate]
Why M-theory has exactly 10+1 dimensions?
Some combinatorics with tensor indices will do.
- 11
3
votes
1
answer
109
views
Complex photon mixed anomaly
$\newcommand{\d}{\mathrm{d}}\newcommand{\U}{\mathrm{U}}\newcommand{\b}[1]{\overline{#1}}\newcommand{\C}{\mathbb{C}}\newcommand{\ex}[1]{\mathrm{e}^{#1}}\newcommand{\i}{\mathrm{i}}$ Consider a free ...
- 3,690
0
votes
0
answers
83
views
Anomalous Hall Conductance by Kubo-Greenwood Formula
The Kubo formula is written below.
$$\sigma_{ij}=\frac{e^2}{\hbar}\int_{BZ}\frac{dk_idk_j}{\left(2\pi\right)^2}\frac{1}{e^{\frac{\epsilon_n-\epsilon_{fermi}}{k_BT}}+1}\sum_{n^{'}\neq n}\frac{2Im\...
- 51
0
votes
0
answers
29
views
Reference for anomalies
I'm reading the preface to the Dover edition of Itzykson and Zuber's "Quantum Field Theory". On page xix, Zuber says
"... Perhaps the most dramatic obsolescence in the book is the ...
0
votes
0
answers
122
views
What would be the implications of an anomalous supersymmetry?
As far as I've studied the literature, there's nothing about the implications of anomalous supersymmetry. There's merely one article that studies anomalous SUSY in the case of $N=1$ SCFT.
Anomalous ...
- 1,131
0
votes
0
answers
41
views
Chern-Simons forms: interpretation and generalizations
Studying again differential geometry, anomalies and topology, I wondered if there is ANY physical interpretations (in terms of QFT or even classical field theory) of the Chern-Simons forms, via vacuum,...
- 6,171
2
votes
1
answer
86
views
Weyl Anomaly for Old Covariant Quantization in String Theory?
In the context of quantization in string theory, the modern approach is the path integral/modern covariant quantization approach. As known from QFT, we fix our gauge and represent the arising Fadeev-...
- 196
3
votes
0
answers
109
views
How to understand this interpretation in the triangle diagram for massive fermions
In the QFT book written by Schwartz, he was calculating the one-loop diagram,
of $\pi\rightarrow\gamma \gamma$ from the Lagrangian:
$$\mathcal{L} = -\frac{1}{4}F^{2}_{\mu\nu}-\frac{1}{2}\phi(\square+...
- 51
0
votes
1
answer
113
views
Chiral symmetry of the Euclidean action for fermions
In the literature, such as QFT Volume-II by Weinberg, p.368, the chiral anomaly is derived using Euclidean path integral. To formulate the question, let's start with the Minkowski space with signature ...
1
vote
1
answer
49
views
Why 't Hooft says: field configuration in Euclidean space that have the vacuum (or a gauge transformation thereof) at the boundary
In Symmetry Breaking through Bell-Jackiw Anomalies G. 't Hooft, Phys. Rev. Lett. 37, 8 – Published 5 July 1976,
't Hooft said that the topological quantum number $n$
$n$ is an integer for all field ...
- 533
1
vote
0
answers
103
views
Axions as goldstone bosons of anomalous $U(1)$ symmetry
In the $m_q \rightarrow 0$ limit the QCD lagrangian has the symmetry $U(N)_V \times U(N)_A$. Including just the two lightest quarks, $N=2$, and looking at the $U(2)_A=SU(2)_A \times U(1)_A$ part, we ...
- 11
3
votes
0
answers
80
views
Why does Tong uses Euclidean Gamma matrices in this step of deriving the Chiral Anomaly?
In David Tong's GT notes on page 137, he uses the trace identity for Euclidean gamma matrices given by
$$\text{Tr}(\gamma^5\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma})=4\epsilon^{\mu\nu\rho\...
- 103
3
votes
1
answer
105
views
Apparent elimination of a 't Hooft anomaly in quantum spin system
The simplest system with a 't Hooft anomaly is the spin $\frac{1}{2}$ system with hamiltonian $\hat{H}=0$. The 't Hooft anomaly follows from the fact that such system has a trivial $SO(3)$ symmetry, ...
- 311
0
votes
0
answers
28
views
Abelian anomaly - does it happen when fermions interact chirally or non-chirally with the gauge fields?
In Weinberg QFT volume 2 p.362, the author says he will calculate the chiral anomaly in a theory where spin $1/2$ fermions interact non-chirally with a set of gauge fields.
An example is the $u$ and $...
- 1,281
1
vote
1
answer
66
views
How did the two copies of the Witt algebra become two copies of the Virasoro algebra in the CFT?
The Virasoro algebra
\begin{equation}
[L_m,L_n]=(m-n) L_{m+n} +\frac{c}{12} (m^3-m) \delta_{m+n,0}
\end{equation}
of the stress energy tensor $T$ was said to follow from the witt algebra of the local ...
- 3,058
2
votes
0
answers
62
views
Anomalous baryon current in the Standard Model (SM) and the stability of free protons within the confines of the SM
In the Standard Model, the baryon number is not exactly conserved due to anomaly but the decay rate is extraordinarily small at ordinary temperatures. Does this make free protons unstable in the ...
- 25.4k
2
votes
0
answers
40
views
How does one arrive at the relation of commutator $\left[M^{-i}, M^{-j}\right]$ of Lorentz generators $M^i$ in terms of the string modes $\alpha_n^i$?
I am reading the book "String theory demystified" by David McMahon.
On page 149, the author discusses the "critical dimension" for superstrings.
the number of spacetime dimensions ...
- 151
2
votes
1
answer
58
views
In calculating the abelian anomaly, why can't we use $D^\mu D_\mu$ as a regulator? - Weinberg QFT vol 2 p.364
In calculating the abelian anomaly of gauge theories based on the method by Fujikawa, the square of the Dirac operator, $(D^\mu \gamma_\mu)^2$, is used. Here $D^\mu$ is the gauge covariant derivative.
...
- 1,281
1
vote
1
answer
59
views
A question about the Dirac operator and zero modes in the book "Mirror Symmetry" by Clay Institute
I have a question about the book "Mirror Symmetry" p.296~298.
Using the notations there, the Dirac operator and its conjugate are denoted as $D_z$ and $D_{\overline{z}}$. In p.297, the book ...
- 1,281
13
votes
3
answers
3k
views
How are anomalies possible?
From Matthew D. Shwartz Quantum Field Theory textbook, he writes:
"Most of the time, a symmetry of a classical theory is also a symmetry of the quantum theory based on the same Lagrangian. When ...
- 1,945
4
votes
0
answers
123
views
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-...
- 61
0
votes
1
answer
107
views
Gauge anomalies?
Why are gauge anomalies so important for any model?
Secondly, any model has to respect the gauge anomalies cancellation requirement?
If this isn't true, then why does one check their model to look ...
- 7
4
votes
1
answer
177
views
Symmetries: from a classical field theory to quantum
My background about this argument:
a) Let's consider a classical field theory, where $\mathcal{L}(\phi(x),\partial_{\mu}\phi_(x))$ is the lagrangian density.
A symmetry is a transformation $\phi(x) \...
- 495
7
votes
1
answer
183
views
Why should a projective representation of a classical symmetry lift to a non-projective representation?
Background
Take a classical system with symmetry $G$. Suppose we can quantize this to a quantum system with Hilbert space $\mathcal{H}$. The state space of the quantum system is given by the ...
- 539
1
vote
1
answer
84
views
The regularization mass in Fujikawa's calculation of axial anomaly
I am reading Fujikawa's paper for axial anomaly:
https://doi.org/10.1103/PhysRevD.21.2848
In equation (2.15), the anomalous part of axial transformation is regularized by
$$\begin{align*}
\mathcal{A}(...
- 13
5
votes
1
answer
212
views
How projective representations can lead to 't Hooft anomalies in quantum mechanics?
In Shao's talk https://youtu.be/2vTvHYYl1Qk?t=1554, he argues that in quantum mechanics "if a symmetry acts projectively on states, then we have a t' Hooft anomaly". But I'm having trouble ...
- 311
2
votes
1
answer
110
views
How can Chiral symmetry protect the mass of a fermion if it's broken by quantization?
Suppose we have a Lagrangian invariant under Chiral symmetry, such as QED with massless fermions:
$$ \mathscr{L} = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \bar{\psi} i \gamma^{\mu} D_{\mu} \psi .$$
In ...
0
votes
1
answer
99
views
Minus sign on the chiral anomaly
I've been going through various derivations of the chiral anomaly for using the Fujikawa method, particularly that in Srednicki's QFT textbook (see chpt. 77 in particular).
A lot of literature ...
- 544
2
votes
1
answer
103
views
Fermion number non-conservation in parallel $E$ and $B$ fields
This is from Problem 19.1 in Peskin and Schroeder.
(a) Show that the Adler-Bell-Jackiw anomaly equation leads to the following law for global fermion number conservation: If $N_R$ and $N_L$ are, ...
- 321
2
votes
0
answers
94
views
How can i calculate the Berry Curvature for the Dirac points in Haldane graphene?
I want to calculate the berry curvature at the Dirac points in graphene with complex next nearest hopping (haldane model) in order to show that it is non-zero at the dirac points and use it to compute ...
0
votes
0
answers
62
views
Chiral anomaly of Weyl fermion is half of Dirac
How can one mathematically see that the anomaly for a Weyl fermion is half of Dirac in the Fujikawa path integral method?
Edit
I do understand that a Dirac fermion is two Weyl fermions. What I wish to ...
- 53
0
votes
0
answers
80
views
Local scale invariance without conformal anomaly
I need to know if conformal symmetry can be localized in the same manner that global symmetries like $SU(2)$ is localized and gauge bosons pop up?(I assume the trace anomaly doesn't violate the scale ...
- 1,131
3
votes
0
answers
56
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 ...
- 729
3
votes
0
answers
58
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 ...
- 1,281
2
votes
0
answers
117
views
How do I understand this conformal transformation?
I am learning conformal transformation, and this is by far the most confusing transformation for me.
For the 2D bc system
$$S=\frac{1}{2\pi}\int d^2 z b\overline{\partial}c,$$
we have the ghost ...
- 176
8
votes
2
answers
160
views
What is the "instanton configurations of the gauge field"?
In the study of the abelian chiral anomaly, one finds that it can be written as the total derivative of a vector operator:
$$\int \mathcal{A}(x)d^4x\propto\int\epsilon_{\mu\nu\rho\sigma}F^{\mu\nu}F^{\...
- 5,225
6
votes
1
answer
275
views
Polchinski's first derivation of the Weyl anomaly
So, i've been reading volume 1 of Polchinski's String Theory text book and have a doubt.
His first derivation of the Weyl anomaly goes as follows:
From dimensional analysis, we know that:
$$\begin{...
- 63
1
vote
0
answers
44
views
Existence of Weyl invariant regulator for bosonic string theory
In sec $(3.4)$ Polchinksi says
It is easy to preserve the diff- and Poincare invariances in the quantum theory. For example, one may define the gauge fixed path integral using a Pauli-Villars ...
- 2,903
2
votes
0
answers
68
views
Can the singlet anomaly be derived from gauge anomaly inflow?
A Dirac spinor field is a left/right pair of chiral spinor fields, and $N$ free massless Dirac spinors have a $U(N)_L\times U(N)_R$ symmetry that cannot be fully gauged. The singlet anomaly in ...
- 52.6k
1
vote
2
answers
157
views
How can we show the Lorentz symmetry is not anomalous in $\phi^{4}$ theory?
how can I show in a lagrangian with scalar fields and $\phi^{4}$ interaction, the energy-momentum tensor isn't anomalous?
- 11
4
votes
0
answers
156
views
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 ...
- 808