A Note on the Geometry of CHL Heterotic Strings

TL;DR

This paper explores the geometric structure of the moduli space of heterotic string compactifications on a two-dimensional torus, revealing how different heterotic string theories relate through topologically non-trivial bundles.

Contribution

It provides a geometric interpretation of the eight-dimensional CHL heterotic string using topologically non-trivial vector bundles and shows the equivalence of their moduli spaces.

Findings

The moduli space of CHL heterotic strings can be understood via non-trivial vector bundles.

The moduli spaces of $E_8\times E_8$ and $\Spin(32)/Z_2$ heterotic strings coincide.

Topologically non-trivial bundles explain disconnected components of the moduli space.

Abstract

We present a few remarks on disconnected components of the moduli space of heterotic string compactifications on $T_2$. We show in particular how the eight dimensional CHL heterotic string can be understood in terms of topologically non-trivial $E_8\times E_8$ and $\Spin(32)/Z_2$ vector bundles over the torus, and that the respective moduli spaces coincide.