Elliptic genera of Berglund-H\"ubsch models

TL;DR

This paper establishes a connection between the elliptic genus of Berglund-H"ubsch models and vertex algebra supertraces, demonstrating it as a weak Jacobi form and revealing mirror symmetry relations.

Contribution

It proves the elliptic genus matches a vertex algebra supertrace and shows it is a weak Jacobi form, also relating mirror pairs.

Findings

Elliptic genus equals vertex algebra supertrace.

Elliptic genus is a weak Jacobi form.

Mirror models have elliptic genera equal up to a sign.

Abstract

We match the elliptic genus of a Berglund-H\"ubsch model with the supertrace of $y^{J[0]}q^{L[0]}$ on a vertex algebra $V_{{\bf 1}, {\bf 1}}$. We show that it is a weak Jacobi form and the elliptic genus of one theory is equal to (up to a sign) the elliptic genus of its mirror.