Cosets of Meromorphic CFTs and Modular Differential Equations

TL;DR

This work develops a generalized coset framework whereby a meromorphic self-dual theory at central charge $c=24$ serves as the numerator and an affine subtheory as the denominator to produce consistent coset CFTs. By relating the modular differential equation parameters through the coset construction, it explains the observed connections between $\ell=0$ and $\ell=2$ two-character theories and explicitly constructs the $\ell=2$ family; it further yields new three- and four-character CFTs by cosets with $c=24$ self-dual theories. The approach provides concrete, verifiable character expressions and positivity of degeneracies via MDE analysis, and supplies a large set of new RCFTs potentially useful for the RCFT classification program. Overall, it links modular-invariance constraints, coset symmetries, and explicit spectral data to expand the known landscape of rational CFTs with small numbers of characters.

Abstract

Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are constructed. The same method also gives rise to interesting new examples of CFTs with three and four characters.