$S$-matrix in permutation orbifolds

Abstract

For a fixed positive integer $k$, any element $g$ of the permutation group $S_k$ acts on the tensor product vertex operator algebra $V^{\otimes k}$ in the obvious way. In this paper, we determine the $S$-matrix of ${\left(V^{\otimes k}\right)}^G$ if $G=⟨g⟩$ is the cyclic group generated by $g=\left(1,2,\cdots ,k\right).$

20 pages