All Questions
Tagged with anomaly or quantum-anomalies
393 questions
5
votes
2
answers
1k
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{...
- 4,737
5
votes
0
answers
210
views
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
0
answers
236
views
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 (...
- 129k
4
votes
2
answers
594
views
Gravitational and gauge-gravitational anomalies in ${\cal N}=1$ $D=4$ supergravity coupled to a SUSY gauge theory with chiral matter
When people talk about the first superstring revolution they often mention the miraculous cancellation of anomalies via the Green-Schwarz mechanism. My question is whether such a string-theoretic ...
- 576
4
votes
1
answer
328
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) \...
- 587
4
votes
1
answer
201
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 ${\cal N}=2$ ...
- 232
4
votes
1
answer
326
views
What does $B+L$ anomaly have to do with a phase redefinition of the left-handed quark field?
According to this answer, the reason why $SU(2)_L$ weak theory does not have a theta vacuum is because any theta term can be reabsorbed with a phase redefinition of the left-handed quark field.
...
- 2,646
4
votes
1
answer
373
views
"The operators with nontrivial vacuum expectation values have to soak up the zero modes associated to the anomaly."
I was reading ref.1, where one can read (emphasis mine)
... the vacuum expectation value $\langle \mathcal O_{\phi_1}\cdots \mathcal O_{\phi_\ell}\rangle$ vanishes unless
$$
\sum_{k=1}^\ell\...
4
votes
1
answer
492
views
chiral anomaly and translation symmetry in 1+1D
A Luttinger liquid at low energies can be captured by Dirac fermions in 1+1D, where the two component fermion field is given by
$$\Psi(x)=\left(\begin{array}{c}\psi_R(x)\\\psi_L(x)\end{array}\right),$$...
- 1,515
4
votes
1
answer
277
views
Anomalies and determinant bundle curvature
I heard that anomalies and curvature of determinant bundle are related. Namely, curvature of determinant bundle is related to Chern-Simons form (which are involved in description of gauge anomalies).
...
- 546
4
votes
2
answers
1k
views
Traces in different representation
I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental ...
- 672
4
votes
1
answer
201
views
Anomalous global symmetry in non-gauge theories
I’m a bit confused on the effects of anomalous global symmetries. So take for instance the following theory
$$\mathscr{L}=\partial_\mu\phi\partial^\mu\phi^*+i\bar{\psi}\gamma_\mu\partial^\mu\psi-y \...
- 181
4
votes
1
answer
219
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 $$\mathcal{T}^2= (-1)^B$$ ...
- 417
4
votes
1
answer
520
views
Loop counting for determinants and anomalies
I am trying to understand an argument for why anomalies are one-loop exact, given by Bilal in Lectures on Anomalies. The relevant paragraph is reproduced here:
Let us first explain why the anomaly ...
- 485
4
votes
1
answer
310
views
2D anomaly-free condition for a gauge theory
Take a $SU(2)$ gauge theory in 2d spacetime, say there are $n_1$ left-handed Weyl fermion in spin-1 written as
$$
1_L,
$$
and $n_0$ left-handed Weyl fermion in spin-0 written as
$$
0_L .
$$
and $n_{1/...
- 4,376
4
votes
1
answer
264
views
Simple explanation of the QCD VEV in terms of instantons
I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
- 8,971
4
votes
1
answer
916
views
Why do we study anomalies with the triangle diagram?
This is a very basic question.
Why do we study anomalies by means of the triangle diagram, i.e. the tree-point function of gauge/global currents and not with, for instance, a two point function?
In ...
- 2,237
4
votes
1
answer
298
views
Regularization and renomalization in the lightcone quantization of bosonic string
This question relates to this link. But I still don't understand it >_<
In Polchinski's string theory vol I, p. 22, there is a divergence term (when $\epsilon \rightarrow 0$) in the zero point ...
- 6,451
4
votes
1
answer
225
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}(...
- 1,911
4
votes
1
answer
162
views
Momentum replacement in the axial anomaly calculation in dimensional regularisation (‘t Hooft prescription)
I have been studying the axial anomaly and everywhere I see the calculation of the triangle loop using dimensional regularisation (see for example pages 661-664 of section 19.2 of Peskin). In the ‘t ...
4
votes
1
answer
220
views
Can a gauge anomaly be *removed* by quantum corrections?
Consider a classical gauge field coupled to a vector field $j^\mu$. Gauge invariance requires that $\mathcal A_\mathrm{cl}:=\partial_\mu j^\mu$ vanishes:
$$
\mathcal A_\mathrm{cl}\equiv 0
$$
In other ...
4
votes
1
answer
650
views
Anomalies of QCD
I have come across the following statement:
The anomalies of QCD cannot be reproduced by a collection of free fermions
carrying $U(1)_V$, $SU(N_f)_L$ and $SU(N_f)_R$ quantum numbers. That is why ...
- 719
4
votes
1
answer
980
views
Axial anomaly in QCD VS axial anomaly in current algebra QCD
I would like to understand the distinction between an axial anomaly in QCD (Theta Vacuum: axion -> 2 gluons) and an axial anomaly in QCD of current (Chern–Simons term: pion->two photons, photon->three ...
- 215
4
votes
1
answer
1k
views
Why are critical dimensions and central charge linkable?
From wikipedia:
"In order for a string theory to be consistent, the worldsheet theory must be conformally invariant. The obstruction to conformal symmetry is known as the Weyl anomaly and is ...
4
votes
1
answer
738
views
anomalous chiral symmetry and the $\bar\theta$ parameter
I am studying anomalous $U(1)$'s, related to the strong CP problem, and I have some trouble with the origin of the parameter $\bar{\theta}$.
We start with the QCD Lagrangian with the topological ...
- 609
4
votes
0
answers
47
views
Resources on Advanced Topics in Standard Model: nonperturbative phenomena, phase transitions, etc
I'm interested in some books on Standard Model physics that discuss advanced topics in quantum field theory. By this I mean topics such as instantons, sphalerons, and friends, the electroweak phase ...
4
votes
0
answers
57
views
Gauge Anomalies General scenario using Fujikawa Method
I would like to ask a question about Gauge Anomalies and how we can extract them through the Fujikawa method, without using the general triangle diagram as proposed by Weinberg Volume 2 Chapter 22.3.
...
- 111
4
votes
0
answers
141
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 ...
- 1,774
4
votes
0
answers
202
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
4
votes
0
answers
206
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 ...
- 868
4
votes
0
answers
121
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 ...
- 81
4
votes
0
answers
256
views
’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 ...
- 5,737
4
votes
0
answers
92
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 ...
- 3,544
4
votes
0
answers
312
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 ...
- 261
4
votes
0
answers
194
views
Mathematics of Anomalies in QFT [duplicate]
As a mathematics student interested in theoretical physics, I found it very hard to study about anomalies in QFT in standard physics texts. They concentrate on particular examples (like chiral anomaly)...
4
votes
0
answers
224
views
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
137
views
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
$$
Q_{0}(t) = \int d^{3}\mathbf r J_{0}(\...
- 8,971
4
votes
0
answers
115
views
Inconsistency in regularization with parallel and perpendicular momenta
In deriving the axial anomaly Peskin and Schroeder use dimensional regularization, continuing loop momenta to $ 4 - \epsilon $ dimenstions. The loop momenta can now be split into pieces ``parallel'' ...
- 9,005
4
votes
0
answers
660
views
Effective field theories and gauge anomalies cancellation
Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
- 8,971
4
votes
0
answers
516
views
Anomaly for Majorana fermion?
In 4-spacetime dimension, is there U(1) gauge field chiral anomaly associated with Majorana fermion (or I am not sure if it is equivalent, majorana representation)? Besides, I have read from several ...
- 531
4
votes
0
answers
187
views
Some fundamental results in QFTs [closed]
In quantum theory we have some principles that guides us, e.g. Pauli's principle. What I am after in this question is a list of fundamental results, be it equation or identities that must hold in a ...
- 5,629
3
votes
3
answers
1k
views
Question on Conformal Field Theory
Since every question has to be asked in a seperate topic,
I'm asking a question refering to the following topic:
Beginners questions concerning Conformal Field Theory
In particular I'm referring to ...
- 391
3
votes
1
answer
1k
views
The non-abelian chiral anomaly and one-loop diagrams higher than the triangle one
Suppose chiral fermions $\psi$ interacting with gauge fields $A_{\mu,L/R}$. With $P_{L/R} \equiv \frac{1\mp\gamma_{5}}{2}$ and $t_{a,L/R}$ denoting the generators, the corresponding action reads
$$
S =...
- 8,971
3
votes
1
answer
8k
views
Why are there specifically 10, 11, or 26 dimensions in string theory? [duplicate]
I know that current string theories state that there are 10, 11, or 26 spacetime dimensions in superstring theory, M-theory, and bosonic string theory, respectively. But when I looked up why those ...
3
votes
1
answer
174
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 ...
- 4,376
3
votes
2
answers
182
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 ...
3
votes
1
answer
135
views
If a regularization procedure respects a symmetry, is this symmetry unbroken in perturbation theory?
I read in this paper the statement that a proof that SUSY is preserved in perturbation theory would be the existence of a regularization procedure which respects SUSY (for a particular theory).
Is ...
- 2,022
3
votes
1
answer
674
views
Hermiticity of Dirac Operator $\gamma^{\mu}D_{\mu}$ and Expansion in eigenmodes
I'm interested to know under what conditions $\gamma^{\mu}D_{\mu}$ is a hermitian operator.
I am studying the Fujikawa method of anomalies and I see that many sources have different answers for this. ...
- 2,816
3
votes
1
answer
776
views
Is it the chiral anomaly which is solely responsible for having instanton effects (and therefore, the $\theta-$term) in the QCD action?
$\textbf{Fact 1}$ In principle, the QCD Lagrangian should contain a Lorentz invariant, gauge invariant, dimension-4 term $\sim\theta \text{Tr}[F^{\mu\nu}\tilde{F}_{\mu\nu}]$. This term, however, is ...
- 27.2k
3
votes
1
answer
137
views
How is the dimensionful renornalization scale $\mu$ related to break of scale invariance in String Theory?
In the $7.1.1$ of David Tong's String Theory notes it is said the following about regularization of Polyakov action in a curved target manifold:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
- 1,330