Differential operators for elliptic genera

TL;DR

This paper develops modular covariant differential operators for weak Jacobi forms using N=2 superconformal field theories, aiding in characterizing elliptic genera and constraining extremal models.

Contribution

It introduces a new class of differential operators based on Zhu's recursion relations generalized to N=2 theories, linking them to elliptic genera.

Findings

Differential operators characterize elliptic genera of N=2 minimal models.

Operators can be used to constrain extremal N=2 superconformal theories.

The approach generalizes Zhu's recursion relations to N=2 superconformal field theories.

Abstract

Using the generalisation 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 characterise the elliptic genera of N=2 superconformal minimal models, and sketch how they can be used to constrain extremal N=2 superconformal field theories.