Discretization of 3d gravity in different polarizations

Understand

We study the discretization of 3d gravity with $\Lambda=0$ following the loop quantum gravity framework.

• In the process, we realize that different choices of polarization are possible.
• This allows to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework.
• We also identify the classical non-trivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps.