Modular differential equations and null vectors

Abstract

We show that every modular differential equation of a rational conformal field theory comes from a null vector in the vacuum Verma module. We also comment on the implications of this result for the consistency of the extremal self-dual conformal field theories at c=24 k.

28 pages, LaTeX, v2: added appendix containing details of proof; version published in JHEP, v3: corrected typos in appendix

References in corpus (11)

• Quantum Gravity Partition Functions in Three Dimensions
• Three-Dimensional Gravity Revisited
• Logarithmic torus amplitudes
• Constraints on extremal self-dual CFTs
• Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster)
• AdS_3 Partition Functions Reconstructed
• Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity
• Partition Functions of Three-Dimensional Pure Gravity
• Bulk perturbations of N=2 branes
• Vector-valued modular functions for the modular group and the hypergeometric equation
• Monster symmetry and Extremal CFTs

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