  Should nature be supersymmetric, then it will be described by Quantum
Supergravity at least in some energy regimes. The currently most advanced
description of Quantum Supergravity and beyond is Superstring Theory/M-Theory
in 10/11 dimensions. String Theory is a top-to-bottom approach to Quantum
Supergravity in that it postulates a new object, the string, from which
classical Supergravity emerges as a low energy limit. On the other hand, one
may try more traditional bottom-to-top routes and apply the techniques of
Quantum Field Theory. Loop Quantum Gravity (LQG) is a manifestly background
independent and non-perturbative approach to the quantisation of classical
General Relativity, however, so far mostly without supersymmetry. The main
obstacle to the extension of the techniques of LQG to the quantisation of
higher dimensional Supergravity is that LQG rests on a specific connection
formulation of General Relativity which exists only in D+1 = 4 dimensions. In
this Letter we introduce a new connection formulation of General Relativity
which exists in all space-time dimensions. We show that all LQG techniques
developed in D+1 = 4 can be transferred to the new variables in all dimensions
and describe how they can be generalised to the new types of fields that appear
in Supergravity theories as compared to standard matter, specifically
Rarita-Schwinger and p-form gauge fields.
