Momentum Lattice for CHL String

TL;DR

This paper introduces a lattice analogue for CHL string theory, exploring its symmetries, gauge groups, dualities, and moduli spaces across various dimensions, connecting to dual theories like Type IIA, M Theory, and F Theory.

Contribution

It constructs a lattice framework for CHL string, analyzes its symmetries and dualities, and classifies boundary components of moduli spaces in multiple dimensions.

Findings

Symmetries of the lattice match perturbative spectrum symmetries.

Explicit description of S-duality action on background fields.

Moduli spaces align with those of dual theories in various dimensions.

Abstract

We propose some analogue of the Narain lattice for CHL string. The symmetries of this lattice are the symmetries of the perturbative spectrum. We explain in this language the known results about the possible gauge groups in compactified theory. For the four-dimensional theory, we explicitly describe the action of S-duality on the background fields. We show that the moduli spaces of the six, seven and eight-dimensional compactifications coincide with the moduli spaces of the conjectured Type IIA, M Theory and F Theory duals. We classify the rational components of the boundary of the moduli space in seven, eight and nine dimensions.