Massive U(1)s and Heterotic Five-Branes on K3

TL;DR

This paper analyzes heterotic string compactifications on K3 surfaces with various gauge backgrounds and five-branes, deriving conditions for U(1) masses and Green-Schwarz terms, and providing explicit supersymmetric examples.

Contribution

It systematically studies heterotic K3 compactifications with Abelian/non-Abelian backgrounds and five-branes, deriving mass formulas and Green-Schwarz terms, and presents explicit supersymmetric models.

Findings

U(1) masses depend on bundle Chern classes

Generalized Green-Schwarz terms constrain five-brane actions

Explicit supersymmetric models on toric K3s are constructed

Abstract

We systematically consider heterotic SO(32) and E8 x E8 compactifications on K3 with Abelian and non-Abelian backgrounds as well as an arbitrary number of five-branes. The masses of the U(1) factors depend on the first Chern classes of the bundles and some combinatorial factors specifying the embedding in SO(32) or E8. The form of the generalised Green-Schwarz counter-terms in six dimensions constrains the possible heterotic five-brane actions. Some supersymmetric examples on K3 realisations as toric complete intersection spaces with up to three explicit two-forms are given.