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Questions tagged [affine-lie-algebra]

An infinite dimensional Lie algebra. This tag is not to be confused with the [tag:lie-algebra] tag.

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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 ...
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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 ...
84 views

Affine space for Minkowski space time

I'm studying Minkowski space time (M4) and they say it's a 4 dimensions real affine space. M4 is an affine space so there is a non-empty set A, a 4 dimension real vector space V, and there is a ...
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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 ...
177 views

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 ...
159 views

Emergence of $SU(2)\times SU(2)$ at the self-dual point in bosonic string theory

I want to understand the derivation of the equations 8.3.11 in Polchinski Vol 1. I can understand that at the self-dual point the Kaluza-Klein momentum index $n$, the winding number $w$, and the ...
Intuitively I feel that if you compactified open bosonic strings on a product of $n$ circles such that each radius is fine-tuned to the self-dual point then the CFT of these $n$ world-sheet fields ...