# Quarter-BPS states in orbifold sigma models with ADE singularities

## TL;DR

This paper investigates the elliptic genera of orbifold conformal field theories with ADE surface singularities, revealing their structure, scaling properties, and connections to geometric resolutions and other genera.

## Contribution

It introduces a detailed analysis of elliptic genera in orbifold sigma models with ADE singularities, linking algebraic, geometric, and modular properties.

## Key findings

- Elliptic genera from twisted sectors exhibit a consistent scaling property.
- Decomposition of elliptic genera encodes information about exceptional rational curves.
- Connections established between twisted sector elliptic genera, twining genera, and Hodge elliptic genera.

## Abstract

We study the elliptic genera of two-dimensional orbifold CFTs, where the orbifolding procedure introduces du Val surface singularities on the target space. The N=4 character decompositions of the elliptic genus contributions from the twisted sectors at the singularities obey a consistent scaling property, and contain information about the arrangement of exceptional rational curves in the resolution. We also discuss how these twisted sector elliptic genera are related to twining genera and Hodge elliptic genera for sigma models with K3 target space.