On Superconformal Field Theories Associated to Very Attractive Quartics

TL;DR

This paper explores superconformal field theories linked to specific quartic hypersurfaces in CP^3, generalizing previous models and connecting them to mirror moonshine phenomena on K3 surfaces.

Contribution

It introduces 'very attractive quartics' and demonstrates how to explicitly construct associated superconformal field theories, extending prior geometric interpretations.

Findings

Confirmed geometric interpretation of Gepner model (2)^4 on Fermat quartic

Linked superconformal theories to mirror moonshine phenomena on K3

Generalized construction to new classes of quartic hypersurfaces

Abstract

We study N=(4,4) superconformal field theories with left and right central charge c=6 which allow geometric interpretations on specific quartic hypersurfaces in CP^3. Namely, we recall the proof that the Gepner model (2)^4 admits a geometric interpretation on the Fermat quartic and give an independent cross-check of this result, providing a link to the "mirror moonshine phenomenon" on K3. We clarify the role of Shioda-Inose structures in our proof and thereby generalize it: We introduce "very attractive quartics" and show how on each of them a superconformal field theory can be constructed explicitly.