A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6

TL;DR

This paper explores the structure of the moduli space of N=(4,4) superconformal field theories with central charge 6, identifying known models, their geometric interpretations, and dualities within the context of K3 surfaces.

Contribution

It provides a refined description of the moduli space, locates various models including orbifolds and Gepner models, and establishes T-duality and geometric interpretations within conformal field theory.

Findings

Identified locations of orbifold and Gepner models in the moduli space.

Proved T-duality for Z_2 orbifolds.

Established geometric interpretation of the Gepner model (2)^4.

Abstract

We study the moduli space ${\cal M}$ of N=(4,4) superconformal field theories with central charge c=6. After a slight emendation of its global description we find the locations of various known models in the component of ${\cal M}$ associated to K3 surfaces. Among them are the Z_2 and Z_4 orbifold theories obtained from the torus component of ${\cal M}$. Here, SO(4,4) triality is found to play a dominant role. We obtain the B-field values in direction of the exceptional divisors which arise from orbifolding. We prove T-duality for the Z_2 orbifolds and use it to derive the form of ${\cal M}$ purely within conformal field theory. For the Gepner model (2)^4 and some of its orbifolds we find the locations in ${\cal M}$ and prove isomorphisms to nonlinear sigma models. In particular we prove that the Gepner model (2)^4 has a geometric interpretation with Fermat quartic target space.