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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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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How do Weyl Transformations act on the Hamiltonian?

in the following I will not be very precise, I would just like to paint the rough picture. My confusion is the following: When one considers a classically Weyl invariant theory defined by an Action $S$...
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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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1 answer
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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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4 votes
1 answer
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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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9 votes
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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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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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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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8 votes
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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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6 votes
1 answer
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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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3 answers
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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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2 answers
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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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$\gamma^5$ 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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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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5 votes
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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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