Symmetries of quantum spacetime in three dimensions

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\mathrm{\Lambda }$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of ${\mathfrak{so}}_q(4)$, with $q=\exp (i\hslash \sqrt{\mathrm{\Lambda }}/2\kappa )$. By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping $\kappa$ finite, we obtain the kappa-Poincaré algebra of the flat quantum spacetime symmetries.

Figure 1

The logical steps of the paper.