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<p>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 [<b>n</b>, <i>ℓ</i>], with <b>n</b> being the number of characters and <i>ℓ</i> the Wronskian index. The modular linear differential equation (MLDE) that the characters of a RCFT solve are labelled similarly. All RCFTs with a given [<b>n</b>, <i>ℓ</i>] solve the modular linear differential equation (MLDE) labelled by the same [<b>n</b>, <i>ℓ</i>]. With the goal of classifying [<b>3, 3</b>] and [<b>3, 4</b>] 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 <i>&lt; c ≤</i> 32. Amongst these [<b>3, 3</b>] character-like solutions, we find pairs of them that form coset-bilinear relations with meromorphic CFTs/characters of central charges 16<i>,</i> 24<i>,</i> 32<i>,</i> 40<i>,</i> 48<i>,</i> 56<i>,</i> 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 [<b>3, 3</b>] CFTs. In the [<b>3, 4</b>] case, we obtain nine character-like solutions each of which is a [<b>2, 2</b>] character-like solution adjoined with a constant character.</p>

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Classifying three-character RCFTs with Wronskian index equalling 3 or 4

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  • 发表日期：

    2026年1月2日

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  • Chethan N. Gowdigere,
  • Sachin Kala,
  • Jagannath Santara

摘要

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.