Real twistings are 2-line bundles

TL;DR

This paper develops a bicategory framework for super 2-line bundles over graded Lie groupoids, unifying various geometric models of twistings in (Real) K-theory, including bundle gerbes and twisted extensions.

Contribution

It introduces a comprehensive bicategory model that encompasses multiple existing models of twistings in (Real) K-theory, providing a unified geometric framework.

Findings

Unified framework for twistings of (Real) K-theory.

Includes models like bundle gerbes, twisted groupoid extensions, and algebra bundles.

Demonstrates how various models are special cases within the bicategory.

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.