All Questions
Tagged with affine-lie-algebra lie-algebra
9
questions
0
votes
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answer
114
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Central Charge Calculation of $SL_k(2,\mathbb{R})$ WZW Model
According to P. Francesco et al. conformal field theory book the central charge of the enveloping Virasoro algebra of the affine Lie algebra $\hat{g}_k$ corresponding with Lie algebra $g$ which ...
1
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0
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60
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String theory coset-space theories in the text book by Becker, Becker and Schwarz (BBS)
I am reading the string theory and M-theory by Becker, Becker and Schwarz (BBS). And I came across a section in chapter 3 called coset-space theories (after equation 3.58)
At the beginning of this ...
- 442
3
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0
answers
90
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Applications of Dynkin Diagrams in Physics [closed]
I've been studying Dynkin Diagrams for a while, but I can't grasp what are the applications in physics.
Can anyone help me understand where can we use Dynkin Diagrams in particle physics to "...
- 1,213
2
votes
0
answers
62
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Symmetry generating commutator in Witten's treatment of WZW model
In 'Non-abelian Bosonization in Two Dimensions', Witten writes down the commutation relations between currents and fields of the WZW model in equation (33):
\begin{equation}
\bigg[\frac{1}{2\pi}\bigg(\...
- 1,171
2
votes
0
answers
66
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Why does Witten not include higher order quantum corrections when quantizing Poisson brackets in the WZW model?
In 'Non-abelian Bosonization in Two Dimensions', Witten argues that the Poisson brackets of the currents that generate the $G\times G$ symmetry of the WZW model give rise to a Kac-Moody algebra upon ...
- 1,171
3
votes
2
answers
245
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Kac-Moody algebra from WZW model via Poisson brackets
In 'Non-abelian Bosonization in Two Dimensions', Witten shows that the Poisson brackets of the currents that generate the $G\times G$ symmetry of the WZW model give rise to a Kac-Moody algebra upon ...
- 1,171
1
vote
2
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178
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Half Witt algebra
I have the following Lie algebra which is generated by $\{L_n|n\geq 0\}.$ It satisfies the following commutation rule
$$ \Big[ L_i ,L_j \Big]=\frac18 \frac{(2i+2j-1)(2j-2i)}{(2j+1)(2i+1)}L_{i+j-1}-\...
- 113
1
vote
0
answers
434
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Free field (Wakimoto) representation in 2d CFT
This question is more a request for explanations. I'm reading now the Di Francesco book in attempt to understand how the free field representations of 2d CFTs are constructed. The first steps in ...
- 2,921
12
votes
2
answers
2k
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Geometric/Visual Interpretation of Virasoro Algebra
I've been trying to gain some intuition about Virasoro Algebras, but have failed so far.
The Mathematical Definition seems to be clear (as found in http://en.wikipedia.org/wiki/Virasoro_algebra). I ...
- 1,233