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arXiv · 2607.18375

Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap

Arpit Das·Sunil Mukhi
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Abstract

Characters of rational conformal field theories solve modular linear differential equations labelled by their order and the Wronskian index $\ell$. Direct classification of admissible solutions by solving MLDEs becomes increasingly difficult at higher $\ell$ -- where movable poles and accessory parameters appear. In this work we introduce differential operators that relate higher-$\ell$ solutions to lower-$\ell$ ones while preserving modular covariance and integrality of the \(q\)-series. In rank two, this generates all allowed Wronskian sectors from the Mathur--Mukhi--Sen equation. In rank three and higher, it reduces the construction of higher-$\ell$ quasi-characters to simpler equations with lower $\ell$. This gives an efficient new route for organising candidate RCFT characters, and more generally quasi-characters, across the Wronskian tower. As an application, we apply our construction to prove a previously conjectured property on the signs of $\ell=2$ quasi-characters in rank 2.

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Arpit Das, Sunil Mukhi. 2026-07-20. Unlocking the Wronskian Tower: A Simplification of the Holomorphic Modular Bootstrap. https://arxiv.org/abs/2607.18375

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