Freedom and Constraints in the K3 Landscape

TL;DR

This paper classifies and constructs six-dimensional string vacua with specific gauge groups and matter content using lattice embeddings, enabling efficient model building in the K3 compactification landscape.

Contribution

It introduces a lattice-based classification method for magnetized brane compactifications on K3, allowing explicit and efficient construction of models with desired gauge and matter properties.

Findings

Classification of solutions via lattice embeddings.

Explicit construction of models with specified gauge groups.

Efficient 'dial-a-model' approach for model building.

Abstract

We consider "magnetized brane" compactifications of the type I/heterotic string on K3 with U(1) background fluxes. The nonabelian gauge group and matter content of the resulting six-dimensional vacua are parameterized by a matrix encoding a lattice contained within the even, self-dual lattice Gamma^{3,19}. Mathematical results of Nikulin on lattice embeddings make possible a simple classification of such solutions. This approach makes it possible to explicitly and efficiently construct models in this class with a particular allowed gauge group and matter content, so that one can immediately "dial-a-model" with desired properties.