New variables for classical and quantum (super)-gravity in all dimensions

Supergravity was originally introduced in the hope of finding a theory of gravity without the shortcoming of perturbative non-renormalisability. Although this goal does not seem to have been reached today (with the possible exception of d = 4, N = 8 Supergravity [1]), Superstring theories are argued to reproduce 10d Supergravities as their low energy limits and thus provide a UV-completion of those theories. Loop Quantum Gravity (LQG) on the other hand is a manifestly background independent and non-perturbative approach to the quantisation of General Relativity, however presently limited to four spacetime dimensions. In order to make contact between these two approaches to quantum gravity, we extend the techniques of LQG to higher dimensions and new matter fields appearing in Supergravity theories. The immediate applications of our framework for further research are comparisons between symmetry reduced sectors of those two theories, namely cosmology and black holes.