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arXiv · 2211.04201

Vertex operator for generalised Kac--Moody algebras associated to the two-sphere and the two-torus

Rutwig Campoamor-Stursberg·Michel Rausch de Traubenberg
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Abstract

We pursue our study of generalised Kac-Moody and Virasoro algebras defined on compact homogeneous manifolds. Extending the well-known Vertex operator in the case of the two-torus or the two-sphere, we obtain explicit bosonic realisations of the semi-direct product of the extension of Kac-Moody and Virasoro algebras on $\mathbb S^1 \times \mathbb S^1$ and $\mathbb S^2$, respectively. As for the fermionic realisation previously constructed, in order to have well defined algebras, we introduce, beyond the usual normal ordering prescription, a regulator and regularise infinite sums by means of the Riemann $\zeta$-function.

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Rutwig Campoamor-Stursberg, Michel Rausch de Traubenberg. 2022-11-08. Vertex operator for generalised Kac--Moody algebras associated to the two-sphere and the two-torus. https://doi.org/10.1142/s021773232250239x

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