# The geometry of Casimir W-algebras

Abstract : Let $\mathfrak{g}$ be a simply laced Lie algebra, $\widehat{\mathfrak{g}}_1$ the corresponding affine Lie algebra at level one, and $\mathcal{W}(\mathfrak{g})$ the corresponding Casimir W-algebra. We consider $\mathcal{W}(\mathfrak{g})$-symmetric conformal field theory on the Riemann sphere. To a number of $\mathcal{W}(\mathfrak{g})$-primary fields, we associate a Fuchsian differential system. We compute correlation functions of $\widehat{\mathfrak{g}}_1$-currents in terms of solutions of that system, and construct the bundle where these objects live. We argue that cycles on that bundle correspond to parameters of the conformal blocks of the W-algebra, equivalently to moduli of the Fuchsian system.
Type de document :
Pré-publication, Document de travail
13 pages. 2017

https://hal-cea.archives-ouvertes.fr/cea-01600023
Contributeur : Emmanuelle De Laborderie <>
Soumis le : lundi 2 octobre 2017 - 16:34:29
Dernière modification le : jeudi 15 mars 2018 - 15:05:16

### Identifiants

• HAL Id : cea-01600023, version 1
• ARXIV : 1707.05120

### Citation

Raphaël Belliard, Bertrand Eynard, Sylvain Ribault. The geometry of Casimir W-algebras. 13 pages. 2017. 〈cea-01600023〉

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