Geometric interpretation of the large N=4 index

TL;DR

This paper provides a geometric interpretation of the large N=4 index in WZW models, linking spectral flow orbits of RR ground states to differential forms on the target space using holomorphic differentials with torsion.

Contribution

It introduces a novel geometric framework for understanding the large N=4 index through differential forms and spectral flow in WZW models.

Findings

States in the index are spectral flow orbits of RR ground states

Differential forms with torsion clarify geometric meaning of states

Provides a geometric interpretation of the large N=4 index

Abstract

We study WZW models with the large N=4 superconformal symetry. Our main result is a geometric interpretation of the large N=4 index. In particular, we find that states contributing to the index belong to spectral flow orbits of special RR ground states. We use (anti-)holomorphic differentials with torsion to clarify the geometric meaning of these states in terms of differential forms on the target space.