2023/08/02 by Chethan N. Gowdigere, Gowdigere, Chethan N., Sachin Kala +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2308.01149
openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the Mathur-Mukhi-Sen (MMS) classification scheme for rational conformal field theories (RCFTs), a RCFT is identified by a pair of non-negative integers [n, ℓ], with n being the number of characters and ℓ the Wronskian index. The modular linear differential equation (MLDE) that the characters of a RCFT solve are labelled similarly. All RCFTs with a given [n, ℓ] solve the modular linear differential equation (MLDE) labelled by the same [n, ℓ]. With the goal of classifying [3,3] and [3,4] CFTs, we set-up and solve those MLDEs, each of which is a three-parameter non-rigid MLDE, for character-like solutions. In the former case, we obtain four infinite families and a discrete set of 15 solutions, all in the range 0 < c ≤ 32. Amongst these [3,3] character-like solutions, we find pairs of them that form coset-bilinear relations with meromorphic CFTs/characters of central charges 16, 24, 32, 40, 48, 56, 64. There are six families of coset-bilinear relations where both the RCFTs of the pair are drawn from the infinite families of solutions. There are an additional 23 coset-bilinear relations between character-like solutions of the discrete set. The coset-bilinear relations should help in identifying the [3,3] CFTs. In the [3,4] case, we obtain nine character-like solutions each of which is a [2,2] character-like solution adjoined with a constant character.