Classifying three-character RCFTs with Wronskian index equalling 3 or 4
CN Gowdigere, S Kala, J Santara - arXiv preprint arXiv:2308.01149, 2023 - arxiv.org
CN Gowdigere, S Kala, J Santara
arXiv preprint arXiv:2308.01149, 2023•arxiv.orgIn the Mathur-Mukhi-Sen (MMS) classification scheme for rational conformal field theories
(RCFTs), a RCFT is identified by a pair of non-negative integers $\mathbf {[n,\ell]} $, with
$\mathbf {n} $ being the number of characters and $\mathbf {\ell} $ the Wronskian index. The
modular linear differential equation (MLDE) that the characters of a RCFT solve are labelled
similarly. All RCFTs with a given $\mathbf {[n,\ell]} $ solve the modular linear differential
equation (MLDE) labelled by the same $\mathbf {[n,\ell]} $. With the goal of classifying …
(RCFTs), a RCFT is identified by a pair of non-negative integers $\mathbf {[n,\ell]} $, with
$\mathbf {n} $ being the number of characters and $\mathbf {\ell} $ the Wronskian index. The
modular linear differential equation (MLDE) that the characters of a RCFT solve are labelled
similarly. All RCFTs with a given $\mathbf {[n,\ell]} $ solve the modular linear differential
equation (MLDE) labelled by the same $\mathbf {[n,\ell]} $. With the goal of classifying …
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 , with being the number of characters and the Wronskian index. The modular linear differential equation (MLDE) that the characters of a RCFT solve are labelled similarly. All RCFTs with a given solve the modular linear differential equation (MLDE) labelled by the same . With the goal of classifying and 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 solutions, all in the range . Amongst these character-like solutions, we find pairs of them that form coset-bilinear relations with meromorphic CFTs/characters of central charges . 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 coset-bilinear relations between character-like solutions of the discrete set. The coset-bilinear relations should help in identifying the CFTs. In the case, we obtain nine character-like solutions each of which is a character-like solution adjoined with a constant character.
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