Flat equivariant gerbes: holonomies and dualities

Abstract

We examine the role of global topological data associated to choices of holonomy for flat gauge fields in string compactification. Our study begins with perturbative string compactification on compact flat manifolds preserving 8 supercharges in 5 dimensions. By including non-trivial holonomy for Wilson lines in the heterotic string and for the B-field gerbe in the type II string we find worldsheet dualities that relate these backgrounds to other string compactifications. While our simple examples allow for explicit analysis, the concepts and some of the methods extend to a broader class of compactifications and have implications for string dualities, perturbative and otherwise.

arXiv comment65 pages, tikz figures; v2: typos corrected

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• Decomposition, condensation defects, and fusion
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Unifying the 6D $\mathcal{N}=(1,1)$ String Landscape
• Flat F-theory and friends