String Theory on K3 Surfaces

TL;DR

This paper characterizes the moduli space of N=(4,4) string theories with K3 surfaces, revealing the full symmetry group and connecting classical and quantum geometric perspectives, including mirror symmetry implications.

Contribution

It provides a comprehensive description of the K3 moduli space, identifying its symmetry group and integrating classical and quantum geometric approaches.

Findings

The symmetry group is the full integral orthogonal group of an even unimodular lattice.

A unified description of the moduli space from classical and quantum viewpoints.

Implications for mirror symmetry in algebraic K3 surfaces.

Abstract

The moduli space of N=(4,4) string theories with a K3 target space is determined, establishing in particular that the discrete symmetry group is the full integral orthogonal group of an even unimodular lattice of signature (4,20). The method combines an analysis of the classical theory of K3 moduli spaces with mirror symmetry. A description of the moduli space is also presented from the viewpoint of quantum geometry, and consequences are drawn concerning mirror symmetry for algebraic K3 surfaces.