Non-Geometric T-Duality as Higher Groupoid Bundles with Connections

Abstract: We describe T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects of geometric and half-geometric T-dualities can be described in terms of higher geometry. We extend their construction in two ways. First, we endow the higher geometries with adjusted connections, which allow us to discuss explicit formulas for the metric and the Kalb-Ramond field of a T-background. Second, we extend the principal 2-bundles to augmented 2-groupoid bundles, which accommodate the scalar fields arising in T-duality along several directions as well as $Q$- and $R$-fluxes. Our description is manifestly covariant under the full T-duality group $\mathsf{GO}(n,n;\mathbb{Z})$, and it has interesting physical and mathematical implications.