论文标题
与二球和两螺旋相关的广义kac--moody代数的顶点操作员
Vertex operator for generalised Kac--Moody algebras associated to the two-sphere and the two-torus
论文作者
论文摘要
我们对按紧凑的均匀流形定义的广义KAC-MOODY和VIRASORO代数进行研究。 在两道或两次球员的情况下，扩展了著名的顶点操作员，我们获得了$ \ Mathbb S^1 \ Mathbb s^1 $ s^1 $ and $ \ Mathbb s^2 $ s^2 $ s^2 $ s^2 $ s^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB S^1 \ MATHBB s^1 \ MATHBB S^1 \ MATHBB s^2 $。至于先前构建的费米子实现，为了具有明确定义的代数，我们在通常的正常订购处方，调节器并通过riemann $ζ$函数正规化无限总和。
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 $ζ$-function.
