Fermionic Sum Representations for the Virasoro Characters of the Unitary Superconformal Minimal Models

TL;DR

This paper derives fermionic sum representations for the Virasoro characters of unitary superconformal minimal models, connecting algebraic identities with combinatorial and statistical models.

Contribution

It introduces new fermionic sum formulas for superconformal characters and relates them to generalized Rogers-Ramanujan identities.

Findings

Fermionic sum representations for N=1 superconformal Virasoro characters.

Finitizated identities linking corner transfer matrix polynomials with fermionic forms.

Derivation of generalized Rogers-Ramanujan identities from these representations.

Abstract

We present fermionic sum representation for the general Virasoro character of the unitary minimal superconformal series ($N=1$). Example of the corresponding ``finitizated" identities relating corner transfer matrix polynomials with fermionic companions is considered. These identities in the thermodynamic limit lead to the generalized Rogers-Ramanujan identities.