All Questions
12 questions
3
votes
1
answer
89
views
How to confirm that a QFT is a conformal field theory (CFT) at the quantum level?
My question is: Given a QFT, what's the usual/reliable/logical way to confirm that it's a CFT at the quantum level? Here are some explanations about why I ask this question.
I have learned a lot about ...
- 349
1
vote
0
answers
144
views
Trying to derive chiral anomaly in 2D from Feynman diagrams in position space
Trying to understand the Chiral anomaly, I decided to explore the simplest example of a holomorphic fermion in 2D in a background electromagnetic field $A\text{d}z+\bar{A}\text{d}\bar{z}$. The ...
- 3,985
20
votes
2
answers
7k
views
The phrase "Trace Anomaly" seems to be used in two different ways. What's the relation between the two?
I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing.
The first way I've seen it used is in the manner, for ...
- 3,532
9
votes
1
answer
1k
views
Anomalous Ward Identities and anomalous dimensions
Let us consider an action $S[\phi,\partial\phi]$ which is classically invariant under a transformation group $G$. The associated Noether current $\mathcal{J}^\mu$ is classically conserved, namely $\...
- 2,237
5
votes
1
answer
1k
views
Ambiguity in Beta Functions (2-loop)
Beyond one-loop, the beta function of a QFT is scheme dependent. I would like to understand better this ambiguity.
The easiest thing to say is that you haven't calculated something physical, so of ...
- 2,707
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
$$
S =...
- 8,971
9
votes
1
answer
271
views
How do anomalies work in the causal formulation of QFT?
In the Epstein-Glaser formulation of a QFT, the would-be divergences are taken care of by meticulously splitting the distributions that appear in the construction of the $S$-matrix (or correlation ...
1
vote
0
answers
180
views
$Z_1=Z_2$ without Ward-Takahashi identity?
In the renormalization of QED, the way that $Z_1=Z_2$ is treated e.g. in Schwartz is by first giving a simple "heuristic argument" based on gauge invariance (in the beginning of section 19.5) before ...
- 121
3
votes
1
answer
463
views
Index theorem and UV and IR face of chiral anomaly
The index theorem in theory with fermions and gauge fields implies the relation between the index $n_{+}-n_{-}$ of Dirac operator and the integral $\nu$ over EM field chern characteristic class: $$ \...
- 8,971
6
votes
1
answer
1k
views
$U(1)$ abelian/axial/chiral anomaly in 4D
I am reading $U(1)$ abelian/axial/chiral anomaly in 3+1 dimensions using the path integral method (Fujikawa). Am I wrong in assuming that the anomaly can be cancelled by introducing a counter term in ...
- 311
1
vote
1
answer
396
views
Why does renormalization need an unbroken symmetry?
Common wisdom is that for a QFT to be renormalizable it must be invariant under a symmetry transformation. Why does renormalization need an unbroken symmetry? Which is the first publication that ...
- 11
2
votes
0
answers
144
views
Anomalies from a Renormaization Group Equation (RGE)
This is an approach to anomalies which seems unfamiliar to me..
Firstly what is this function $W$ which seems to satisfy the equation, $\frac{\partial W }{\partial g^{\mu \nu} } = \langle T_{\mu \nu}...
- 4,581