Hecke Relations in Rational Conformal Field Theory

Abstract

We define Hecke operators on vector-valued modular forms of the type that appear as characters of rational conformal field theories (RCFTs). These operators extend the previously studied Galois symmetry of the modular representation and fusion algebra of RCFTs to a relation between RCFT characters. We apply our results to derive a number of relations between characters of known RCFTs with different central charges and also explore the relation between Hecke operators and RCFT characters as solutions to modular linear differential equations. We show that Hecke operators can be used to construct an infinite set of possible characters for RCFTs with two independent characters and increasing central charge. These characters have multiplicity one for the vacuum representation, positive integer coefficients in their $q$ expansions, and are associated to a two-dimensional representation of the modular group which leads to non-negative integer fusion coefficients as determined by the Verlinde formula.

arXiv commentv3: additional small typos corrected. Should agree with version published in JHEP

References in corpus (8)

• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Vertex operator algebras, Higgs branches, and modular differential equations
• On the Classification of Modular Fusion Algebras
• The intermediate vertex subalgebras of the lattice vertex operator algebras
• Two-dimensional RCFT's without Kac-Moody symmetry
• On the Quantum Invariant for the Spherical Seifert Manifold
• Modular Invariance and Uniqueness of Conformal Characters
• Fusion Algebras Induced by Representations of the Modular Group

Cited by in corpus (27)

• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• IIB flux non-commutativity and the global structure of field theories
• Towards a Classification of Two-Character Rational Conformal Field Theories
• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Modular Constraints on Superconformal Field Theories
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Conformal Field Theories with Sporadic Group Symmetry
• Rational CFT With Three Characters: The Quasi-Character Approach
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
• Discreteness and Integrality in Conformal Field Theory
• Wronskian Indices and Rational Conformal Field Theories
• The Most Irrational Rational Theories
• Curiosities above c = 24
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• On Classification of Fermionic Rational Conformal Field Theories
• Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors
• Monster Anatomy
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Meromorphic Cosets and the Classification of Three-Character CFT
• Defect Partition Function from TDLs in Commutant Pairs
• Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs
• Galois Conjugation and Multiboundary Entanglement Entropy
• New meromorphic CFTs from cosets
• Gapped boundaries of fermionic topological orders and higher central charges
• Ramanujan's influence on string theory, black holes and moonshine
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs