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arXiv · 2211.04199

Fermion realisations of generalised Kac--Moody and Virasoro algebras associated to the two-sphere and the two-torus

Rutwig Campoamor-Stursberg·Michel Rausch de Traubenberg
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Abstract

Using the notion of extension of Kac-Moody algebras for higher dimensional compact manifolds recently introduced in [1], we show that for the two-torus $\mathbb S^1 \times \mathbb S^1$ and the two-sphere $\mathbb S^2$, these extensions, as well as extensions of the Virasoro algebra can be obtained naturally from the usual Kac-Moody and Virasoro algebras. Explicit fermionic realisations are proposed. In order to have well defined generators, beyond the usual normal ordering prescription, we introduce a regulator and regularise infinite sums by means of Riemann $\zeta-$function.

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Rutwig Campoamor-Stursberg, Michel Rausch de Traubenberg. 2022-11-08. Fermion realisations of generalised Kac--Moody and Virasoro algebras associated to the two-sphere and the two-torus. https://doi.org/10.1142/s0217732322502406

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