2025/07/09 by Arpit Das, Sunil Mukhi, Das, Arpit +1 · 1 citation
Computer Science · Mathematics · #semigroups and automata theory #Algebraic structures and combinatorial models #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.2507.07170
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 an 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∼(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.