Towards a Classification of Two-Character Rational Conformal Field Theories

Abstract

We provide a simple and general construction of infinite families of consistent, modular-covariant pairs of characters satisfying the basic requirements to describe two-character RCFT. These correspond to solutions of generic second-order modular linear differential equations. To find these solutions, we first construct "quasi-characters" from the Kaneko-Zagier equation and subsequent works by Kaneko and collaborators, together with coset dual generalisations that we provide in this paper. We relate our construction to the Hecke images recently discussed by Harvey and Wu.

arXiv comment64 pages, typos corrected, proofs now provided for two claims that were previously conjectures, final version to appear in JHEP

References in corpus (14)

• Infinite Chiral Symmetry in Four Dimensions
• Meromorphic c=24 Conformal Field Theories
• Vertex operator algebras, Higgs branches, and modular differential equations
• On Modular Invariant Partition Functions of Conformal Field Theories with Logarithmic Operators
• On Fusion Rules in Logarithmic Conformal Field Theories
• Hecke Relations in Rational Conformal Field Theory
• On 2d Conformal Field Theories with Two Characters
• The intermediate vertex subalgebras of the lattice vertex operator algebras
• Two-dimensional RCFT's without Kac-Moody symmetry
• Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories
• Conformal characters and the modular representation
• On classification of extremal non-holomorphic conformal field theories
• Modular differential equations for characters of RCFT
• Universal RCFT Correlators from the Holomorphic Bootstrap

Cited by in corpus (24)

• Holomorphic modular bootstrap revisited
• Poincaré Series, 3d Gravity and Averages of Rational CFT
• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Rational CFT With Three Characters: The Quasi-Character Approach
• Quantum stabilizer codes, lattices, and CFTs
• Bootstrapping Fermionic Rational CFTs with Three Characters
• 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
• Fake Z
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• On Classification of Fermionic Rational Conformal Field Theories
• Meromorphic Cosets and the Classification of Three-Character CFT
• Defect Partition Function from TDLs in Commutant Pairs
• Classification of extremal vertex operator algebras with two simple modules
• New meromorphic CFTs from cosets
• Two approaches to the holomorphic modular bootstrap
• Quasi-Characters in $\widehat{su(2)}$ Current Algebra at Fractional Levels
• Three Dimensional Topological Field Theories and Nahm Sum Formulas
• Modular linear differential equations for four-point sphere conformal blocks
• Contour Integrals and the Modular S-Matrix
• Rényi entropy of single-character CFTs on the torus