All Questions
Tagged with quantum-anomalies renormalization
19
questions
1
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0
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64
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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
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1
answer
123
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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:
$$\tag{7.3} S= \frac{1}{4\pi \alpha'} \int d^2\sigma \ ...
- 1,290
1
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0
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124
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Trying to derive chiral anomaly in 2D from Feynman diagrams in position space
Trying to understand the Chiral anomaly, I decided to explore the simplest example of a holomorphic fermion in 2D in a background electromagnetic field $A\text{d}z+\bar{A}\text{d}\bar{z}$. The ...
- 3,895
4
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131
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Normalization of zero point energy in string theory
Following Joe Polchinski’s Little Book of String, page 12, he use the sum $$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
1
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1
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254
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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. ...
- 516
3
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1
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374
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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 ...
- 8,490
8
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1
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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
1
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172
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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
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1
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267
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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
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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 $\...
- 2,187
3
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1
answer
997
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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 =...
- 8,891
3
votes
1
answer
436
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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: $$ \...
- 8,891
6
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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
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143
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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}...
- 4,561
5
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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 ...
- 2,657