Rational CFT With Three Characters: The Quasi-Character Approach

Abstract

Quasi-characters are vector-valued modular functions having an integral, but not necessarily positive, q-expansion. Using modular differential equations, a complete classification has been provided in arXiv:1810.09472 for the case of two characters. These in turn generate all possible admissible characters, of arbitrary Wronskian index, in order two. Here we initiate a study of the three-character case. We conjecture several infinite families of quasi-characters and show in examples that their linear combinations an generate admissible characters with arbitrarily large Wronskian index. The structure is completely different from the order two case, and the novel coset construction of arXiv:1602.01022 plays a key role in discovering the appropriate families. Using even unimodular lattices, we construct some explicit three-character CFT corresponding to the new admissible characters.

arXiv commentTypos corrected and references added. Final version, to appear in JHEP, 29 pages

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Cited by in corpus (15)

• Poincaré Series, 3d Gravity and Averages of Rational CFT
• Holomorphic modular bootstrap revisited
• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Discreteness and Integrality in Conformal Field Theory
• Wronskian Indices and Rational Conformal Field Theories
• Surface defects, flavored modular differential equations and modularity
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• Meromorphic Cosets and the Classification of Three-Character CFT
• New meromorphic CFTs from cosets
• Two approaches to the holomorphic modular bootstrap
• Modular linear differential equations for four-point sphere conformal blocks
• Quasi-Characters in $\widehat{su(2)}$ Current Algebra at Fractional Levels
• Rényi entropy of single-character CFTs on the torus