Holomorphic quasimodular bootstrap

In this paper, we propose a generalization to the holomorphic modular bootstrap approach featuring flavored modular differential equations arising from null states of the algebra. The approach can be applied to rational and the more general quasilisse chiral algebras that arise in the study of four-dimensional superconformal field theories. The transformation property of the flavored equations reveals hidden and universal effective action of the modular group and spectral flow on the null states. As shown in examples, the equations compute the full ordinary and nonordinary spectra both in the untwisted and the twisted sector.