General aspects of heterotic string compactifications on stacks and gerbes

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.

72 pages, LaTeX; v2: typos fixed, references added; v3: updated appendix

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Cited by in corpus (16)

• Notes on generalized global symmetries in QFT
• Undoing decomposition
• Notes on nonabelian (0,2) theories and dualities
• Decomposition in diverse dimensions
• Anomaly resolution via decomposition
• Quantum symmetries in orbifolds and decomposition
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Orbifolds by 2-groups and decomposition
• A generalization of decomposition in orbifolds
• Chiral operators in two-dimensional (0,2) theories and a test of triality
• Decomposition in Chern-Simons theories in three dimensions
• Landau-Ginzburg models for certain fiber products with curves
• Bagger-Witten line bundles on moduli spaces of elliptic curves
• Decomposition squared
• Chern-Simons theory, decomposition, and the A model
• Global aspects of moduli spaces of 2d SCFTs