Twisted Elliptic Genera of N=2 SCFTs in Two Dimensions

TL;DR

This paper explores twisted elliptic genera in two-dimensional N=2 superconformal field theories, revealing their properties, applications to orbifolds, and connections to dualities and mathematical identities.

Contribution

It introduces the concept of twisted elliptic genera for N=2 SCFTs with fractional U(1) charges and proves an ADE generalization of the quintuple product identity.

Findings

Analyzed properties of twisted elliptic genera and indices.

Applied results to orbifold models and duality phenomena.

Proved an ADE generalization of the quintuple product identity.

Abstract

The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and the associated twisted Witten indices are investigated with due attention to their behaviors in orbifoldization. Our findings are illustrated by and applied to several concrete examples. We give a better understanding of the duality phenomenon observed long before for certain Landau-Ginzburg models. We revisit and prove an old conjecture of Witten which states that every ADE Landau-Ginzburg model and the corresponding minimal model share the same elliptic genus. Mathematically, we establish ADE generalizations of the quintuple product identity.