Appell-Lerch Sums and N=2 Moduli

TL;DR

This paper explores the connection between Appell-Lerch sums and the moduli space of certain N=2 elliptic curves, revealing their role in the fermionic aspects of the moduli problem.

Contribution

It demonstrates that the fermionic component of the moduli of odd-framed N=2 elliptic curves is governed by Appell-Lerch sums, linking mock modular forms to geometric moduli.

Findings

Appell-Lerch sums control fermionic moduli

Connection between mock modular forms and elliptic curve moduli

Insights into N=2 elliptic curve structures

Abstract

We study moduli of odd-framed $\mathcal{N}=2$ elliptic curves subject to certain conditions, and show that the fermionic part of the moduli problem is essentially controlled by the Appell-Lerch sum, familiar from the theory of mock modular forms.