Modular differential equations for characters of RCFT

Abstract

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the operator algebra. Besides describing effective algorithmic procedures, we illustrate our methods on an explicit example.

13 pages

References in corpus (4)

• Modular differential equations and null vectors
• Constraints on extremal self-dual CFTs
• Conformal characters and the modular representation
• Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity

Cited by in corpus (9)

• Towards a Classification of Two-Character Rational Conformal Field Theories
• Modular Constraints on Superconformal Field Theories
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Wronskian Indices and Rational Conformal Field Theories
• Vector-Valued Rademacher Sums and Automorphic Integrals
• Universal RCFT Correlators from the Holomorphic Bootstrap
• Meromorphic Cosets and the Classification of Three-Character CFT
• Two approaches to the holomorphic modular bootstrap
• Character Vectors of Strongly Regular Vertex Operator Algebras