The DSR-deformed relativistic symmetries and the relative locality of 3D quantum gravity

TL;DR

This paper demonstrates that the relative-locality framework effectively describes the DSR-deformed symmetries and noncommutative spacetime structures emerging in 3D quantum gravity, providing insights into dual-gravity lensing phenomena.

Contribution

It shows how the relative-locality framework can incorporate the curved momentum space and noncommutative spacetime features of 3D quantum gravity.

Findings

DSR-deformed Poincaré symmetries are characterized in 3D quantum gravity.

The framework explains the noncommutative spacetime structure.

Relative locality leads to dual-gravity lensing effects.

Abstract

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.