All Questions
Tagged with quantum-anomalies renormalization
19
questions
18
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 ...
- 3,492
9
votes
1
answer
267
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 ...
9
votes
1
answer
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 $\...
- 2,197
8
votes
1
answer
242
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Viewing anomalous dimensions in RG as a quantum anomaly
Other than sharing the word “anomalous”, both the anomalous dimension in RG and the more well-known quantum anomalies (such as chiral anomaly) share a common feature. These are violations of classical ...
- 1,485
6
votes
1
answer
1k
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$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
6
votes
0
answers
362
views
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 ...
- 913
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 ...
- 2,667
4
votes
1
answer
294
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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 ...
- 6,401
4
votes
0
answers
132
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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 ...
- 1,734
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
$$
S =...
- 8,901
3
votes
1
answer
124
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How is the dimensionful renornalization scale $\mu$ related to break of scale invariance in String Theory?
In the $7.1.1$ of David Tong's String Theory notes it is said the following about regularization of Polyakov action in a curved target manifold:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
- 1,290
3
votes
1
answer
375
views
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 ...
- 8,490
3
votes
1
answer
437
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: $$ \...
- 8,901
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}...
- 4,561
1
vote
1
answer
256
views
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. ...
- 516