General aspects of heterotic string compactifications on stacks and gerbes

TL;DR

This paper explores heterotic string compactifications on stacks and gerbes, revealing their potential for rich model building and analyzing their properties, spectra, and consistency conditions.

Contribution

It provides a general framework for heterotic strings on stacks, classifies gerbe compactifications, and clarifies their relation to known models and dualities.

Findings

Gerbes admit more bundles than spaces, enriching heterotic compactifications.

Certain classes of gerbe compactifications are equivalent to disjoint unions or dual models.

Some gerbe compactifications are perturbatively inconsistent, limiting their novelty.

Abstract

In this paper we work out some basic results concerning heterotic string compactifications on stacks and, in particular, gerbes. A heterotic string compactification on a gerbe can be understood as, simultaneously, both a compactification on a space with a restriction on nonperturbative sectors, and also, a gauge theory in which a subgroup of the gauge group acts trivially on the massless matter. Gerbes admit more bundles than corresponding spaces, which suggests they are potentially a rich playground for heterotic string compactifications. After we give a general characterization of heterotic strings on stacks, we specialize to gerbes, and consider three different classes of `building blocks' of gerbe compactifications. We argue that heterotic string compactifications on one class is equivalent to compactification of the same heterotic string on a disjoint union of spaces, compactification on another class is dual to compactifications of other heterotic strings on spaces, and compactification on the third class is not perturbatively consistent, so that we do not in fact recover a broad array of new heterotic compactifications, just combinations of existing ones. In appendices we explain how to compute massless spectra of heterotic strings on stacks, derive some new necessary conditions for a heterotic string on a stack or orbifold to be well-defined, and also review some basic properties of bundles on gerbes.