Discrete torsion, orbifold elliptic genera, and the chiral de Rham complex

Abstract

Given a compact complex algebraic variety with an effective action of a finite group $G$, and a class $\alpha \in H^2(G,U(1))$, we introduce an orbifold elliptic genus with discrete torsion $\alpha$, denoted $El{l}_{orb}^{\alpha }(X,G,q,y)$. We give an interpretation of this genus in terms of the chiral de Rham complex attached to the orbifold $[X/G]$. If $X$ is Calabi-Yau and $G$ preserves the volume form, $El{l}_{orb}^{\alpha }(X,G,q,y)$ is a weak Jacobi form. We also obtain a formula for the generating function of the elliptic genera of symmetric products with discrete torsion.

References in corpus (1)

• The algebra of discrete torsion