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arXiv · 2507.07170

Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT

Arpit Das·Sunil Mukhi
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Abstract

Rational conformal field theories in 2d have partition functions built from holomorphic characters, whose classification can be addressed via the holomorphic modular bootstrap. This is facilitated by a special basis of ``quasi-characters'' that has been completely classified for rank-2. Suitably combining these to form admissible characters with non-negative integral coefficients $a_n$ depends crucially on the signs and growth of the quasi-character coefficients. We use Frobenius recursion relations for Modular Linear Differential Equations to estimate the growth with $c$ of these coefficients in the region $n\sim\frac{c}{12}$ that is inaccessible to Cardy asymptotics, and to prove rigorously that they have alternating signs that stabilise to a fixed sign at this order. This provides a practical path to obtain candidate RCFT partition functions at arbitrary Wronskian index.

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Arpit Das, Sunil Mukhi. 2025-07-09. Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT. https://arxiv.org/abs/2507.07170

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