A vector-valued modular form construction generates new admissible solutions for rational CFT classification from known RCFTs, reproducing all known two-character solutions with Wronskian indices 6 and 8 while extending to six characters.
Curiosities above c = 24
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Two-dimensional rational CFT are characterised by an integer $\ell$, related to the number of zeroes of the Wronskian of the characters. For two-character RCFT's with $\ell<6$ there is a finite number of theories and most of these are classified. Recently it has been shown that for $\ell \ge 6$ there are infinitely many admissible characters that could potentially describe CFT's. In this note we examine the $\ell=6$ case, whose central charges lie between 24 and 32, and propose a classification method based on cosets of meromorphic CFT's. We illustrate the method using theories on Kervaire lattices with complete root systems. In the process we construct the first known two-character RCFT's beyond $\ell=2$.
fields
hep-th 2years
2025 2verdicts
UNVERDICTED 2representative citing papers
The work proves that quasi-character coefficients have stabilizing alternating signs and estimates their growth near n ~ c/12 via Frobenius recursion on MLDEs, enabling candidate RCFT characters at arbitrary Wronskian index.
citing papers explorer
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Two approaches to the holomorphic modular bootstrap
A vector-valued modular form construction generates new admissible solutions for rational CFT classification from known RCFTs, reproducing all known two-character solutions with Wronskian indices 6 and 8 while extending to six characters.
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Signs, growth and admissibility of quasi-characters and the holomorphic modular bootstrap for RCFT
The work proves that quasi-character coefficients have stabilizing alternating signs and estimates their growth near n ~ c/12 via Frobenius recursion on MLDEs, enabling candidate RCFT characters at arbitrary Wronskian index.