Elliptic Genera of Non-compact Gepner Models and Mirror Symmetry

TL;DR

This paper explores the elliptic genera of non-compact Gepner models, revealing their structure as Jacobi forms, their relation to mock modular forms, and demonstrating mirror symmetry through explicit examples.

Contribution

It introduces a new class of elliptic genera from tensor products of minimal and non-compact models, and demonstrates mirror symmetry explicitly for c=9 orbifold models.

Findings

Elliptic genera form a large class of real Jacobi forms.

Mirror pairs of models have matching elliptic genera including long multiplet contributions.

Liouville and cigar elliptic genera transform into each other under mirror symmetry.

Abstract

We consider tensor products of N=2 minimal models and non-compact conformal field theories with N=2 superconformal symmetry, and their orbifolds. The elliptic genera of these models give rise to a large and interesting class of real Jacobi forms. The tensor product of conformal field theories leads to a natural product on the space of completed mock modular forms. We exhibit families of non-compact mirror pairs of orbifold models with c=9 and show explicitly the equality of elliptic genera, including contributions from the long multiplet sector. The Liouville and cigar deformed elliptic genera transform into each other under the mirror transformation.