All Questions
Tagged with affine-lie-algebra conformal-field-theory
17
questions
1
vote
0
answers
60
views
How to derive WZW model’s energy-momentum tensor? The result is of course the Sugawara construction
I want to know how to derive WZW’s energy-momentum tensor. We know WZW action is
$$
S_{WZW}[g]=\frac{k}{16\pi}\int d^2x Tr(\partial g^{-1}\partial g) - \frac{ik}{24\pi}
\int_B d^3y \epsilon_{abc} Tr(h^...
- 99
0
votes
1
answer
114
views
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 ...
2
votes
0
answers
43
views
WZW primary fields / correlations in terms of current algebra?
Cross-posted from a Mathoverflow thread! Answer there for a bounty ;)
Given the
$\mathfrak{u}_N$ algebra
with generators $L^a$ and commutation relations
$ [L^a,L^b] = \sum_c f^{a,b}_{c} L^c $ ,
the ...
- 726
3
votes
0
answers
170
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WZW model - affine Kac-Moody current algebra from Quantum Group exchange algebra
In `Hidden Quantum Groups Inside Kac-Moody Algebra', by Alekseev, Faddeev, and Semenov-Tian-Shansky, a relationship between quantum groups and affine Kac-Moody algebras is shown for the WZW model.
...
- 1,171
3
votes
1
answer
222
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Kac-Moody primary OPE
I am reading a paper and on page 13-14 (PDF page 15-16), they say that,
The fermionic generators [$G^\pm$ and $\tilde{G}^\pm$] are Virasoro
and affine Kac-Moody primaries with weights $h= 3/2 $ ...
- 721
1
vote
0
answers
97
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The mathematical structure of $\widehat{su(2)}_k$
Some of my colleagues work on CFT's and quantum groups and I hear them talk a lot about $\widehat{su(2)}_k$ algebras. According to them (and the general physics literature) these are what ...
- 1,306
1
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0
answers
252
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How to derive Kac-Moody and Virasoro algebras from their descriptions as central extensions?
I am following the notes (https://arxiv.org/abs/hep-th/9904145) to learn conformal field theory, and want to know how to derive the contributions to the Virasoro and Kac-Moody algebras from the ...
- 726
1
vote
1
answer
301
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Factor of $1/2$ in the Sugawara construction
I'm trying to reproduce the Sugawara construction calculation using this reference (page 14).
The normal-ordering of two local operators is defined as
$$ N(XY)(w)=\frac{1}{2\pi i} \oint_w \frac{dx}{...
- 16.2k
1
vote
2
answers
178
views
Half Witt algebra
I have the following Lie algebra which is generated by $\{L_n|n\geq 0\}.$ It satisfies the following commutation rule
$$ \Big[ L_i ,L_j \Big]=\frac18 \frac{(2i+2j-1)(2j-2i)}{(2j+1)(2i+1)}L_{i+j-1}-\...
- 113
8
votes
0
answers
346
views
Free Field Realization of Current Algebras and its Hilbert space
I have some conceptual confusion regarding the interplay between current algebras, their free field representation and the Hilbert space generated from it.
Let's sketch a simple example, $\mathfrak{...
- 410
4
votes
0
answers
155
views
Geometry of Affine Kac-Moody Algebras
One can reconstruct the unitary irreducible representations of compact Lie groups very beautifully in geometric quantization, using the Kähler structure of various $G/H$ spaces.
Can one perform a ...
user145190
2
votes
1
answer
161
views
Kac-Moody algebra, proof of parameters calculation
I'm following the notes "Ginsparg - Applied Conformal Field Theory" (https://arxiv.org/abs/hep-th/9108028) and I'm stuck on a proof at page 140 about Kac-Moody algebras.
I would like to prove that $\...
- 479
2
votes
0
answers
186
views
Physical meaning of the WZW action and Lagrangian
What is the (super)-WZW term physical meaning? I mean, what is the physical importance of the Wess-Zumino-Witten action/Lagrangian in superstrings/M-theory and or field theory (not stringy if ...
- 6,611
5
votes
1
answer
297
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Conformal invariance in Toda field theories
A standard Toda field theory action will be of the shape:
$$ S_{\text{TFT}} = \int d^2 x~ \Bigg( \frac{1}{2} \langle\partial_\mu \phi, \partial^\mu \phi \rangle - \frac{m^2}{\beta^2} \sum_{i=1}^r ...
- 145
1
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0
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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