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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Why M-theory has eleven dimensions? [duplicate]

Why M-theory has exactly 10+1 dimensions? Some combinatorics with tensor indices will do.
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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 ...
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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\...
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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 ...
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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 ...
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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,...
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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-...
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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+...
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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 ...
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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 ...
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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 ...
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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\...
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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, ...
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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 $...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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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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 ...
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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) \...
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Number of dimensions of the universe according to the string theory [duplicate]

I am not a physicist, but what is the current idea of the number of dimensions of the universe according to the string theory?
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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 ...
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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}(...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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^{\...
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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{...
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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 ...
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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 ...
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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?
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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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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 ...
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What is the difference between AdS and BTZ conditions in (2+1)-D gravity?

On the BCFT, at lower Temperatures, the AdS condition is favored while at higher ones, BTZ conditions are. But, I do not understand how the conditions for either one change the gravitational theory. ...
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With massless fermions, does a finite chiral rotation only affect the coefficient of the theta term?

In quantum electrodynamics (QED), the chiral current is not conserved: $$ \partial_\mu(\overline\psi\gamma^\mu\gamma_5\psi)\sim F\wedge F + \text{mass term}. \tag{1} $$ It would be conserved if the ...
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Why are certain topological effects important in quantum theories but not in classical theories?

At the start of Tong's notes on gauge theory, he explains that in classical theory, electromagnetic potentials (or other gauge potentials) don't have any physical influence except through their field ...
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Can someone give a simple derivation of the gravitational contribution to the fermion chiral anomaly in 3+1 dimension using the Fujikawa method?

Can someone suggest a simple derivation of the gravitational contribution to the fermion chiral anomaly in 3+1 dimension using the Fujikawa method? $\epsilon_{\mu\nu\rho\lambda}R^{\mu\nu}_{\gamma\...
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$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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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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$U(1)_A$ 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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