论文标题
与二球相关的广义kac-moody和virasoro代数的fermion实现
Fermion realisations of generalised Kac--Moody and Virasoro algebras associated to the two-sphere and the two-torus
论文作者
论文摘要
使用kac-moody代数的扩展概念[1]中最近引入的较高尺寸紧凑型流形，我们表明，对于两种责任$ \ mathbb s^1 \ times \ times \ mathbb s^1 $ and Mathbb s^2 $ and Mathbb s^2 $ and extenions and viraSory and viraSory and viraSory and extery and viraSory and extery。和Virasoro代数。提出了明确的费米尼实现。为了拥有明确定义的发电机，除了通常的正常订购处方外，我们还引入了调节器并通过Riemann $ζ-$函数正规化无限总和。
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 $ζ-$function.
