General aspects of heterotic string compactifications on stacks and gerbes

TL;DR

This work analyzes heterotic string compactifications on stacks, with a focus on gerbes, to classify potential new vacua. It identifies three building-block classes: Class I where the gauge bundle is pulled back from the base, leading to a decomposition into a disjoint union of spaces; Class II where a duality relates certain gerbe compactifications to ordinary heterotic strings (notably Spin$(32)/\mathbb{Z}_2$ vs $E_8\times E_8$ cases); and Class III with twisted bundles that often fail perturbative consistency, though some consistent (0,2) SCFTs exist. The paper develops a framework for spectra computation via inertia stacks, discusses necessary (but not yet sufficient) anomaly conditions including level-matching and Fock-vacuum constraints, and presents explicit examples (e.g., toroidal orbifolds and Distler–Kachru models) illustrating the proposed dualities and their limitations. Overall, the results provide a structured picture of what new heterotic vacua can arise from gerbes, highlighting when decomposition and duality apply and when twisted-bundle constructions do not yield viable perturbative theories, while outlining several avenues for future refinement of anomaly constraints. This work thus clarifies the landscape of heterotic compactifications on generalized spaces and sets the stage for further rigorous criteria for consistency.

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.