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Article Dans Une Revue SciPost Physics Année : 2018

The geometry of Casimir W-algebras

Résumé

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.
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hal-02359673 , version 1 (03-04-2024)

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Raphaël Belliard, Bertrand Eynard, Sylvain Ribault. The geometry of Casimir W-algebras. SciPost Physics, 2018, 5 (051), ⟨10.21468/SciPostPhys.5.5.051⟩. ⟨hal-02359673⟩
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