Conway Subgroup Symmetric Compactifications Redux

TL;DR

This paper investigates special toroidal compactifications in heterotic string theory linked to Conway group symmetries, exploring dualities with F-theory and type IIA on K3 surfaces, and provides computational tools for analysis.

Contribution

It extends the study of heterotic compactifications with Conway subgroup symmetries and establishes dualities with F-theory and type IIA K3 models, including explicit examples and computational methods.

Findings

Identified twelve heterotic–type IIA dual pairs with matching symmetries.

Developed a Mathematica package for symmetry and lattice computations.

Confirmed the correspondence of symmetry groups and lattice structures across dual theories.

Abstract

We extend the investigation of special toroidal compactifications of heterotic string theory for which the half-BPS states provide representations of subgroups of the Conway group. We also explore dual descriptions of these theories and find that they are all linked to either F-theory or type IIA string theory on K3 surfaces with symplectic automorphism groups that are the same Conway subgroups as those of the heterotic dual. The matching with type IIA K3 dual theories includes both the matching of symmetry groups and a comparison between the Narain lattice on the heterotic side and the cohomology lattice on the type IIA side. We present twelve examples where we can identify a type IIA dual K3 orbifold theory as the dual description of the heterotic theory. In addition, we include a Mathematica package that performs most of the computations required for these comparisons.