Meromorphic Cosets and the Classification of Three-Character CFT

Abstract

We investigate the admissible vector-valued modular forms having three independent characters and vanishing Wronskian index and determine which ones correspond to genuine 2d conformal field theories. This is done by finding bilinear coset-type relations that pair them into meromorphic characters with central charges 8, 16, 24, 32 and 40. Such pairings allow us to identify some characters with definite CFTs and rule out others. As a key result we classify all unitary three-character CFT with vanishing Wronskian index, excluding $c=8,16$. The complete list has two infinite affine series $B_{r,1},D_{r,1}$ and 45 additional theories. As a by-product, at higher values of the total central charge we also find constraints on the existence or otherwise of meromorphic theories. We separately list several cases that potentially correspond to Intermediate Vertex Operator Algebras.

73 pages

References in corpus (9)

• Holomorphic modular bootstrap revisited
• Bootstrapping Fermionic Rational CFTs with Three Characters
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
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Cited by in corpus (4)

• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Non-Chiral Vertex Operator Algebra Associated To Lorentzian Lattices And Narain CFTs
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Rényi entropy of single-character CFTs on the torus