On loop states in quantum gravity and supergravity

Abstract

The Wilson loop functionals in terms of Ashtekar's variables were the first (formal) solutions to the quantized Hamiltonian constraint of canonical gravity. Here it is shown that the same functionals also solve the supergravity constraints, and some evidence is presented that they are not states of a quantum theory whose classical limit is general relativity. For 2+1 dimensional gravity and supergravity it is shown explicitly how some crucial properties of Einstein gravity are lost when using `densitized' constraints.