Holomorphic quasi-modular bootstrap

TL;DR

This paper refines the holomorphic modular bootstrap approach for classifying rational conformal field theories by using flavored modular differential equations and null state constraints to determine algebra structures and spectra.

Contribution

It introduces flavored refinements and null state constraints that enable complete determination of spectra and reveal hidden algebraic structures.

Findings

Constraints on null states determine algebra structure

Flavored modular differential equations fix spectra in all sectors

Revealed hidden structures among null states and spectral flow

Abstract

Holomorphic modular bootstrap is an approach to classifying rational conformal field theories making use of the modular differential equations. In this paper we explore its flavored refinement. For a class of chiral algebras, we propose constraints on a special null state, which determine the structure of the algebra, and through flavored modular differential equations and quasi-modularity, completely fix the spectra in both the untwisted and twisted sector. Using the differential equations, we reveal hidden structures among null states of the chiral algebras under the modular group action and translation related to spectral flow.