Communications in Number Theory and Physics

Volume 3 (2009)

Number 4

Differential operators for elliptic genera

Pages: 593 – 618



Matthias R. Gaberdiel (Institut für Theoretische Physik, ETH Zürich, Switzerland)

Christoph A. Keller (Jefferson Physical Laboratory, Harvard University)


Using the generalization of Zhu’s recursion relations to $N=2$ superconformal fieldtheories, we construct modular covariant differential operators for weakJacobi forms. We show that differential operators of this type characterizethe elliptic genera of $N=2$ superconformal minimal models, andsketch how they can be used to constrain extremal$N=2$ superconformal field theories.

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