Asymmetric Orbifolds, Rank Reduction and Heterotic Islands

TL;DR

This paper develops a formalism for analyzing rank reduction in heterotic string orbifolds, constructing specific models with minimal moduli, using lattice automorphisms and the Leech lattice.

Contribution

It introduces a general method to study moduli space components with gauge group rank reduction in heterotic orbifolds, including explicit constructions of heterotic islands.

Findings

Constructed six- and four-dimensional heterotic models with no massless moduli besides the dilaton.

Developed a formalism involving the Leech lattice and its automorphisms for analyzing orbifold components.

Provided new insights into gauge symmetry breaking and moduli stabilization in string theory.

Abstract

We consider toroidal asymmetric orbifolds of the heterotic string preserving all 16 supercharges, developing a general formalism to study components of the moduli space characterized by rank reduction of the gauge group. In particular we construct six- and four-dimensional heterotic islands with no massless moduli other than the dilaton. The formalism involves the Leech lattice, its automorphisms and their corresponding invariant and normal, or coinvariant, sublattices.