Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 22 (2026), 059, 53 pages      arXiv:2502.18102      https://doi.org/10.3842/SIGMA.2026.059

Real Twistings are 2-Line Bundles

Tim Lüders a, Lynn Otto b and Konrad Waldorf b
a) Universität Wien, Fakultät für Physik, Boltzmanngasse 5, 1090 Wien, Austria
b) Universität Greifswald, Institut für Mathematik und Informatik, Walther-Rathenau-Str. 47, 17487 Greifswald, Germany

Received May 13, 2025, in final form June 04, 2026; Published online June 18, 2026

Abstract
We construct and study a bicategory of super 2-line bundles over graded Lie groupoids, providing a unified framework for geometric models of twistings of (real) K-theory. The core of our work is to exhibit a wide range of models from the literature as special cases, among them several variants of bundle gerbes (real/equivariant/Jandl), Freed-Moore's twisted groupoid extensions, Freed-Hopkins-Teleman's K-theory twistings, Moutuou's real twistings, Freed's invertible algebra bundles, and Distler-Freed-Moore's orientifold twistings.

Key words: twistings of K-theory; real twistings; Lie groupoid; 2-line bundle; bicategory.

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