Virasoro Representations on Fusion Graphs

TL;DR

This paper explores the relationship between fusion graphs in non-unitary models with specific central charges and Virasoro highest weight modules, revealing an isomorphism between path spaces and these modules.

Contribution

It establishes a novel isomorphism between fusion graph path spaces and Virasoro modules in non-unitary models with central charge c(2,q).

Findings

Path spaces are isomorphic to Virasoro modules.

Applicable to non-unitary models with specific central charges.

Provides a new perspective on fusion graph representations.

Abstract

For any non-unitary model with central charge c(2,q) the path spaces associated to a certain fusion graph are isomorphic to the irreducible Virasoro highest weight modules.