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.
On 2d Conformal Field Theories with Two Characters
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Rational CFT's are classified by an integer $\ell$, the number of zeroes of the Wronskian of their characters in moduli space. For $\ell=0$ they satisfy non-singular modular-invariant differential equations, while for $\ell>0$ the corresponding equations have singularities. We survey CFT's with two characters and $\ell=0,2,3,4$ and verify the consistency, at the level of characters, of some candidate theories with $\ell\ne 0$. For $\ell=2$ there are seven consistents sets of characters. We identify specific combinations of level-1 current algebras that are potential symmetries of the corresponding CFT's.
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UNVERDICTED 3representative citing papers
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) and (3,9) solutions are generated as integer points on a polytope via quasi-char
Admissible solutions to MLDEs with ≤6 characters and c_eff ≤24 are enumerated; tenable ones with good fusion rules are identified, with some linked to specific CFTs and MTC classes.
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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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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) and (3,9) solutions are generated as integer points on a polytope via quasi-char
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Updating the holomorphic modular bootstrap
Admissible solutions to MLDEs with ≤6 characters and c_eff ≤24 are enumerated; tenable ones with good fusion rules are identified, with some linked to specific CFTs and MTC classes.