Fusion rules for the Virasoro algebra of central charge 25

TL;DR

This paper establishes a correspondence between fusion rules of certain Virasoro algebra modules at central charge 25 and tensor rules of finite-dimensional sl(2,C) representations, extending known dualities.

Contribution

It proves that fusion rules for Virasoro modules at central charge 25 match tensor rules for sl(2,C) representations, revealing a new duality.

Findings

Fusion rules correspond to sl(2,C) tensor rules

Extension of duality between central charges 1 and 25

New insight into Virasoro algebra module structure

Abstract

Let $\mathcal{F}_{25}$ be the family of irreducible highest weight modules for the Virasoro algebra of central charge $25$ which are not isomorphic to Verma modules. Let $L(25,0)$ be the Virasoro vertex operator algebra of central charge 25. We prove that the fusion rules for the $L(25,0)$-modules in $\mathcal{F}_{25}$ are in correspondence with the tensor rules for the irreducible finite dimensional representations of $sl(2, \mathbb{C})$, extending the known correspondence between modules for the Virasoro algebras of dual central charges 1 and 25.