New Identities between Unitary Minimal Virasoro Characters

TL;DR

This paper proves new identities between Virasoro characters at levels 3, 4, and 5, revealing connections between different minimal models and implications for superconformal branching rules.

Contribution

It introduces novel identities linking minimal Virasoro characters at levels 3, 4, and 5, and explores their implications for superconformal algebra representations.

Findings

Identities connect Ising and tricritical Ising models via Virasoro characters.

Bilayer relations express tricritical Ising characters in terms of Ising characters.

Implications for branching rules of N=4 superconformal characters are discussed.

Abstract

Two sets of identities between unitary minimal Virasoro characters at levels $m=3,4,5$ are presented and proven. The first identity suggests a connection between the Ising and tricritical Ising models since the $m=3$ Virasoro characters are obtained as bilinears of $m=4$ Virasoro characters. The second identity gives the tricritical Ising model characters as bilinears in the Ising model characters and the six combinations of $m=5$ Virasoro characters which do not appear in the spectrum of the three state Potts model. The implication of these identities on the study of the branching rules of $N=4$ superconformal characters into $\widehat{SU(2)} \times \widehat{SU(2)}$ characters is discussed.