On Equivariant Elliptic Genera of Toric Calabi-Yau 3-folds

TL;DR

This paper demonstrates that equivariant elliptic genera of toric Calabi-Yau 3-folds are generalized weak Jacobi forms and introduces an averaged version that are ordinary weak Jacobi forms, providing explicit formulas.

Contribution

It establishes the modular properties of equivariant elliptic genera and introduces a new averaged genus with explicit formulas, extending previous theoretical predictions.

Findings

Equivariant elliptic genera are generalized weak Jacobi forms.

Averaged equivariant elliptic genera are ordinary weak Jacobi forms.

Explicit formulas for averaged genera match predictions by Eguchi and Sugawara.

Abstract

We show that equivariant elliptic genera of toric Calabi-Yau 3-folds are generalized weak Jacobi forms. We also introduce a notion of averaged equivariant elliptic genera of toric Calabi-Yau 3-folds, and show that they are ordinary weak Jacobi forms given by an explicit formula predicted by Eguchi and Sugawara.