Differential operators for elliptic genera

Abstract

Using the generalization of Zhu's recursion relations to N = 2 superconformal field theories, we construct modular covariant differential operators for weak Jacobi forms. We show that differential operators of this type characterize the elliptic genera of N = 2 superconformal minimal models, and sketch how they can be used to constrain extremal N = 2 superconformal field theories.