Over the last decade there were significant advances in the understanding of quantum gravity coupled to point particles in 3D (2+1-dimensional) spacetime. Most notably it is emerging that the theory can be effectively described as a theory of free particles on a momentum space with anti-deSitter geometry and with noncommutative spacetime coordinates of the type $[x^{ \mu},x^{ \nu}]=i \hbar \ell \varepsilon^{ \mu\nu}_{ \phantom{ \mu\nu}\rho} x^{ \rho}$. We here show that the recently proposed relative-locality curved-momentum-space framework is ideally suited for accommodating these structures characteristic of 3D quantum gravity. Through this we obtain an intuitive characterization of the DSR-deformed Poincar\'e symmetries of 3D quantum gravity, and find that the associated relative spacetime locality is of the type producing dual-gravity lensing.
Categories: hep-th gr-qc