CHL Compactifications Revisited

TL;DR

This paper reviews CHL compactifications, a class of supersymmetry-preserving orbifolds in string theory, highlighting their moduli spaces, dualities, and unique vacua with minimal massless fields, within the broader context of string dualities.

Contribution

It provides a comprehensive review of the CHL compactifications, their moduli spaces, duality properties, and introduces new mathematical curiosities related to their physical implications.

Findings

Existence of moduli spaces with few massless scalars.

Decompactification to ten-dimensional superstring theories.

Presence of electric-magnetic duality in 4D moduli spaces.

Abstract

CHL compactifications are supersymmetry preserving orbifolds of any perturbatively renormalizable and ultraviolet finite ground state of the perturbative string theories: heterotic, type I, or type II, preserving 32, 16, 12, 8, 4, (or zero) supersymmetries, and retaining the perturbative renormalizability and finiteness of the parent string vacuum. In this paper, we review the genesis of the CHL (Chaudhuri-Hockney-Lykken) project within the broader context of the full String/M Duality web, establishing the existence of moduli spaces with a small number of massless scalar fields, the decompactification of such moduli spaces to one of the five ten-dimensional superstring theories, and the appearance of electric-magnetic duality in only the four-dimensional moduli spaces, a 1995 observation due to Chaudhuri & Polchinski. We present two mathematical curiosities easily deduced from the fermionic current algebra representation but whose physical significance is a puzzle: a 4D N=4 heterotic string vacuum with no massless scalar fields other than the dilaton, and a 2D N=8 heterotic string vacuum with no abelian gauge fields, reiterating once more the necessity for a systematic classification of the CHL orbifolds.