Factorized Combinations of Virasoro Characters

TL;DR

This paper explores the factorization of Virasoro characters into basic blocks, introduces the secondary effective central charge, and derives new identities including generalizations of Rogers-Ramanujan identities, with applications in conformal theories.

Contribution

It provides a comprehensive analysis of factorized Virasoro characters, introduces the secondary effective central charge, and derives new character identities using classical mathematical identities.

Findings

Identified all cases of character factorization via Gauss-Jacobi and Watson identities.

Established new identities between different Virasoro characters.

Generalized Rogers-Ramanujan identities within the context of Virasoro models.

Abstract

We investigate linear combinations of characters for minimal Virasoro models which are representable as a products of several basic blocks. Our analysis is based on consideration of asymptotic behaviour of the characters in the quasi-classical limit. In particular, we introduce a notion of the secondary effective central charge. We find all possible cases for which factorization occurs on the base of the Gauss-Jacobi or the Watson identities. Exploiting these results, we establish various types of identities between different characters. In particular, we present several identities generalizing the Rogers-Ramanujan identities. Applications to quasi-particle representations, modular invariant partition functions, super-conformal theories and conformal models with boundaries are briefly discussed.