Moduli Space of CHL Strings

TL;DR

This work constructs the moduli space of CHL strings by an asymmetric $\mathbb{Z}_2$ orbifold of the $E_8\times E_8$ heterotic string, reproducing the rank-reduced, maximally supersymmetric vacua and revealing enhanced symmetry structures such as $(Sp(20))_1$ and $(SO(37-4D))_1$ across spacetime dimensions. It analyzes the momentum lattices, twist sectors, and marginal deformations to show how non-simply-laced and simply-laced algebras arise at special points, connects the $D=8$ case to Narain compactifications, and discusses decompactification limits and potential dualities. In $D=4$, the construction provides evidence for S-duality by showing dual gauge groups appear at the same moduli points, while in $D=6$ it raises puzzles for string-string duality and hints at dual descriptions involving asymmetric orbifolds of Type II theories. Overall, the paper argues that CHL theories inhabit a cohesive moduli space consistent with Narain-like lattices and duality symmetries, motivating further exploration of reduced-rank moduli spaces and their string-theoretic duals.

Abstract

We discuss an orbifold of the toroidally compactified heterotic string which gives a global reduction of the dimension of the moduli space while preserving the supersymmetry. This construction yields the moduli space of the first of a series of reduced rank theories with maximal supersymmetry discovered recently by Chaudhuri, Hockney, and Lykken. Such moduli spaces contain non-simply-laced enhanced symmetry points in any spacetime dimension D<10. Precisely in D=4 the set of allowed gauge groups is invariant under electric-magnetic duality, providing further evidence for S-duality of the D=4 heterotic string.