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

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.

10 pages, detailed description of the structure of the Hilbert space, references added, to appear in Mod. Phys. Lett. A

References in corpus (3)

• An overview of generalised Kac-Moody algebras on compact real manifolds
• Dimensional oxidization on coset space
• Vertex operator for generalised Kac--Moody algebras associated to the two-sphere and the two-torus

Cited by in corpus (1)

• Kac-Moody Algebras on Soft Group Manifolds