Questions tagged [affine-lie-algebra]
An infinite dimensional Lie algebra. This tag is not to be confused with the [lie-algebra] tag.
27
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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
$$
S_{WZW}[g]=\frac{k}{16\pi}\int d^2x Tr(\partial g^{-1}\partial g) - \frac{ik}{24\pi}
\int_B d^3y \epsilon_{abc} Tr(h^...
- 99
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Central Charge Calculation of $SL_k(2,\mathbb{R})$ WZW Model
According to P. Francesco et al. conformal field theory book the central charge of the enveloping Virasoro algebra of the affine Lie algebra $\hat{g}_k$ corresponding with Lie algebra $g$ which ...
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WZW primary fields / correlations in terms of current algebra?
Cross-posted from a Mathoverflow thread! Answer there for a bounty ;)
Given the
$\mathfrak{u}_N$ algebra
with generators $L^a$ and commutation relations
$ [L^a,L^b] = \sum_c f^{a,b}_{c} L^c $ ,
the ...
- 726
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Discretization of derivative of delta function and affine Kac-Moody algebra
In equation (4.16) of https://arxiv.org/abs/1506.06601, a discretization of the (classical) affine Kac-Moody algebra is presented:
$$
\frac{1}{\gamma}\left\{J_{m}^{1}, J^2_{n}\right\}=J_{m}^{1} J_{n}^{...
- 1,171
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
2
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OPE Kac-Moody Currents
We have the following operators:
\begin{align}
J^a(z) = \frac{1}{2}\psi_s^{\dagger}(z)\sigma^a_{s s'}\psi_{s'}(z), \hspace{10 mm} \bar{J}^a(z) = \frac{1}{2}\psi_s^{\dagger}(\bar{z})\sigma^a_{s s'}\...
- 41
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2
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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