S-matrix in orbifold theory

TL;DR

This paper determines the restricted S-matrix for orbifold theories derived from vertex operator algebras and computes specific cases for cyclic permutation orbifolds of prime order.

Contribution

It provides a general method to compute the restricted S-matrix for orbifold vertex operator algebras and explicitly calculates cases for cyclic permutation orbifolds.

Findings

Restricted S-matrix determined for any regular vertex operator algebra and finite automorphism group.

Explicit S-matrix computations for cyclic permutation orbifolds of prime orders.

Enhanced understanding of modular properties in orbifold conformal field theories.

Abstract

The restricted $S$-matrix of $V^G$ is determined for any regular vertex operator algebra $V$ and finite automorphism group $G$ of $V.$ As an application, the $S$-matrices for cyclic permutation orbifolds of prime orders are computed.