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Conformal characters and the modular representation
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Conformal characters and the modular representation
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A general procedure is presented to determine, given any suitable representation of the modular group, the characters of all possible Rational Conformal Field Theories whose associated modular representation is the given one. The relevant ideas and methods are illustrated on two non-trivial examples: the Yang-Lee and the Ising models.
Forward citations
Cited by 4 Pith papers
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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 extendi...
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A differential operator Θ = η^{-4}D relates MLDE solutions across Wronskian sectors, reducing higher-ℓ quasi-character classification in ranks 2 and 3 to ℓ=0 data and proving the ℓ=2 sign conjecture.
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Quasi-Characters for three-character Rational Conformal Field Theories
All (3,0) admissible solutions are expressed via a universal _3F_2 hypergeometric formula; (3,3) solutions are built from them using Bantay-Gannon duality with only 7 of 15 having proper fusion rules, and further (3,6...
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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.
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