Path Spaces and W-Fusion in Minimal Models

TL;DR

This paper derives product forms of Virasoro minimal model characters, relates them to Rogers-Ramanujan identities, and analyzes their path space structure and fusion rules, providing new insights into the algebraic and combinatorial aspects of these models.

Contribution

It introduces a novel factorization of minimal model characters and connects them to Rogers-Ramanujan identities, enhancing understanding of their algebraic and combinatorial structures.

Findings

Product forms of minimal model characters are obtained.

Connections to Rogers-Ramanujan identities are established.

Analysis of path space structure and fusion rules is provided.

Abstract

Product forms of characters of Virasoro minimal models are obtained which factorize into $(2,\odd)\times(3,\even)$ characters. These are related by generalized Rogers-Ramanujan identities to sum forms allowing for a quasiparticle interpretation. The corresponding dilogarithm identities are given and the factorization is used to analyse the related path space structure as well as the fusion of the maximally extended chiral algebra.