Modular S-transforms of chirally deformed CFT partition functions are determined iteratively by second-order OPE poles of the deforming currents, with explicit multiplicities.
Modular differential equations and null vectors
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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.
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Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations
Modular S-transforms of chirally deformed CFT partition functions are determined iteratively by second-order OPE poles of the deforming currents, with explicit multiplicities.