N=4 Characters in Gepner Models, Orbits and Elliptic Genera

TL;DR

This paper analyzes characters of the N=4 superconformal algebra in the context of K3 sigma models, deriving elliptic genera from multiple Gepner models and exploring modular properties and orbit structures.

Contribution

It provides a detailed comparison of elliptic genus computations across different Gepner models and reveals new orbit structures and modular relations.

Findings

Derived elliptic genus expressions for three Gepner models

Identified orbit structures for additional models

Established relations for theta function cubes

Abstract

We review the properties of characters of the N=4 SCA in the context of a non-linear sigma model on $K3$, how they are used to span the orbits, and how the orbits produce topological invariants like the elliptic genus. We derive the same expression for the $K3$ elliptic genus using three different Gepner models ($1^6$, $2^4$ and $4^3$ theories), detailing the orbits and verifying that their coefficients $F_i$ are given by elementary modular functions. We also reveal the orbits for the $1^3 2^2$, $1^4 4$ and $1^2 4^2$ theories. We derive relations for cubes of theta functions and study the function $ {1\over\eta} \sum_{n\in \Z} (-1)^n (6n+1)^k q^{(6n+1)^2 /24} $ for $k=1,2,3,4$.