Towards a Classification of Two-Character Rational Conformal Field Theories

TL;DR

This paper introduces a new framework for classifying two-character rational conformal field theories by constructing solutions to modular differential equations using quasi-characters and coset duals.

Contribution

It presents a general method for generating infinite families of two-character RCFT solutions via modular differential equations and quasi-characters, extending previous work with coset duals and Hecke images.

Findings

Constructed infinite families of RCFT characters satisfying modular covariance.

Linked quasi-characters to solutions of modular differential equations.

Related the construction to Hecke images and coset duals.

Abstract

We provide a simple and general construction of infinite families of consistent, modular-covariant pairs of characters satisfying the basic requirements to describe two-character RCFT. These correspond to solutions of generic second-order modular linear differential equations. To find these solutions, we first construct "quasi-characters" from the Kaneko-Zagier equation and subsequent works by Kaneko and collaborators, together with coset dual generalisations that we provide in this paper. We relate our construction to the Hecke images recently discussed by Harvey and Wu.