Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities

TL;DR

This paper explores fermionic sum representations of characters in specific minimal Virasoro models, deriving new Rogers-Ramanujan type and dilogarithm identities, and discusses methods for constructing more general fermionic representations.

Contribution

It introduces new fermionic sum representations for characters of certain minimal models and derives related Rogers-Ramanujan and dilogarithm identities, expanding the understanding of these models.

Findings

New fermionic sum representations for minimal model characters

Derived Rogers-Ramanujan type identities

Obtained dilogarithm identities for effective central charges

Abstract

Characters and linear combinations of characters that admit a fermionic sum representation as well as a factorized form are considered for some minimal Virasoro models. As a consequence, various Rogers-Ramanujan type identities are obtained. Dilogarithm identities producing corresponding effective central charges and secondary effective central charges are derived. Several ways of constructing more general fermionic representations are discussed.