Fusion rules of Virasoro Vertex Operator Algebras

TL;DR

This paper establishes the fusion rules for a class of Virasoro vertex operator algebras by analyzing their limits from known fusion rules of related algebras, providing a comprehensive understanding of their structure.

Contribution

It proves the fusion rules of $L(c_{1,q},0)$ for all $q extgreater=1$ by deriving them as limits of fusion rules of $L(c_{n,nq-1},0)$ as $n$ approaches infinity.

Findings

Fusion rules for $L(c_{1,q},0)$ are explicitly determined.

Fusion rules are obtained as limits of those for $L(c_{n,nq-1},0)$.

The approach unifies the understanding of fusion rules across different central charges.

Abstract

In this paper we prove the fusion rules of $L(c_{1,q},0)$ for all $q\geq1$. Roughly speaking, we consider $L(c_{1,q},0)$ as the limitation of $L(c_{n,nq-1},0)$, where $n\rightarrow\infty$, and the fusion rules of $L(c_{1,q},0)$ follow as the limitation of the fusion rules of $L(c_{n,nq-1},0)$.