Twining Genera of (0,4) Supersymmetric Sigma Models on K3

TL;DR

This paper computes twining genera for (0,4) supersymmetric sigma models on K3, revealing connections to the sporadic group M24 through explicit examples and localization techniques.

Contribution

It introduces a method to calculate twining genera for (0,4) models on K3 using linear sigma models and localization, linking these models to M24 moonshine.

Findings

Computed explicit twining genera for various instanton embeddings.

Identified consistency with M24 moonshine phenomena.

Demonstrated the use of localization in (0,4) models.

Abstract

Conformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E8xE8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E8xE8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera - elliptic genera with appropriate insertions of discrete symmetry generators in the trace - for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M24.