  We study several aspects of the canonical quantization of supergravity in
terms of the Asthekar variables. We cast the theory in terms of a $GSU(2)$
connection and we introduce a loop representation. The solution space is
similar to the loop representation of ordinary gravity, the main difference
being the form of the Mandelstam identities. Physical states are in general
given by knot invariants that are compatible with the $GSU(2)$ Mandelstam
identities. There is an explicit solution to all the quantum constraint
equations connected with the Chern-Simons form, which coincides exactly with
the Dubrovnik version of the Kauffman Polynomial. This provides for the first
time the possibility of finding explicit analytic expressions for the
coefficients of that knot polynomial.
