Cascade of Special Holonomy Manifolds and Heterotic String Theory

TL;DR

This paper explores heterotic string theory compactified on special holonomy manifolds, analyzing gauge symmetries, holonomy cascades, and their implications for supersymmetry and matter spectra through explicit models.

Contribution

It introduces a detailed study of holonomy cascades and their role in heterotic string compactifications, including modular invariant constructions and spectrum analysis.

Findings

Gauge symmetry F_4 in G_2 compactification

Gauge symmetry so(9) in Spin(7) compactification

Relation between topological numbers and matter multiplicities

Abstract

We investigate hetrotic string theory on special holonomy manifolds including exceptional holonomy G_2 and Spin(7) manifolds. The gauge symmetry is F_4 in a G_2 manifold compactification, and so(9) in a Spin(7) manifold compactification. We also study the cascade of the holonomies: so(8) > Spin(7) > G_2 > su(3) > su(2). The differences of adjoining groups are described by Ising, tricritical Ising, 3-state Potts and u(1) models. These theories are essential for spacetime supersymmetries and gauge group enhancements. As concrete examples, we construct modular invariant partition functions and analyze their massless spectra for G_2 and Spin(7) orbifolds. We obtain the relation between topological numbers of the manifolds and multiplicities of matters in specific representations.