On equivalence between Bose/Fermi Virasoro characters

TL;DR

This paper derives fermionic sum representations for Virasoro characters of specific non-unitary minimal models using the Andrews--Bailey construction, confirming some conjectured expressions.

Contribution

It introduces new fermionic sum formulas for Virasoro characters of non-unitary minimal models, expanding the mathematical understanding of these models.

Findings

Derived fermionic sum representations for ${ m M}(k,kp+p-1)$ and ${ m M}(k,kp+1)$ models.

Confirmed certain conjectured expressions by the Stony Brook group.

Connected Andrews--Bailey construction to Virasoro character representations.

Abstract

On the basis of the Andrews--Bailey construction, we derive fermionic sum representations of Virasoro characters of non unitary minimal models ${\cal M}(k,kp+p-1)$ and ${\cal M}(k,kp+1)$. These expressions include certain expressions conjectured by the Stony Brook group as special cases.