All Questions
Tagged with quantum-anomalies renormalization
20 questions
3
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1
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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
70
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Reference request scale anomaly
Can anyone recommend some books, notes and review-oriented papers on scale anomaly, with a view towards its relation to renormalization? Such as an anomaly perspective on RG, Callan-Symanzik equations ...
3
votes
1
answer
137
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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:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
- 1,330
1
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0
answers
144
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Trying to derive chiral anomaly in 2D from Feynman diagrams in position space
Trying to understand the Chiral anomaly, I decided to explore the simplest example of a holomorphic fermion in 2D in a background electromagnetic field $A\text{d}z+\bar{A}\text{d}\bar{z}$. The ...
- 3,985
4
votes
0
answers
141
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Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$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
1
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1
answer
281
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Is string theory self-consistent? (Conformal anomaly)
Recently I attended a very short course on string theory. We went through the standard presentation in light-cone gauge for brevity. We ‘derived’ the Einstein field equation in the following manner. ...
- 526
3
votes
1
answer
394
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Does the vanishing of the one-loop beta-function imply no running to all orders?
This question sounds ridiculous, but bear with me. I am having a hard time reconciling the following two facts:
Classical global symmetries can become anomalous upon quantization, and the anomalous ...
- 8,582
8
votes
1
answer
246
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Viewing anomalous dimensions in RG as a quantum anomaly
Other than sharing the word “anomalous”, both the anomalous dimension in RG and the more well-known quantum anomalies (such as chiral anomaly) share a common feature. These are violations of classical ...
- 1,515
1
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0
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180
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$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
9
votes
1
answer
271
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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 ...
9
votes
1
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1k
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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
3
votes
1
answer
1k
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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
463
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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
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$U(1)$ 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
2
votes
0
answers
144
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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
5
votes
1
answer
1k
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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
4
votes
1
answer
298
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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
20
votes
2
answers
7k
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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
1
vote
1
answer
396
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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
6
votes
0
answers
369
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Conformal anomaly of free scalar in 2D
I'm trying to calculate the conformal anomaly $c$ of a free scalar on a 2-sphere. I've seen other, indirect ways to do this, but since this is a free theory I feel like it should be possible to see ...
- 933