PHYSICAL STATES IN D = 3, N = 2 SUPERGRAVITY

To clarify some issues raised by D'Eath's recent proposal for the phys ical states of N = 1 supergravity in four dimensions, we study pure (t opological) N = 2 supergravity in three dimensions, which is formally very similar, but much easier to solve. The wave functionals solving t he quantum constraints can be understood in terms of arbitrary functio ns on the space of moduli and supermoduli, which is not Hausdorff. We discuss the implications for the wave functionals and show that these are not amenable to expansions in fermionic coordinates, but can serve as lowest-order solutions to the quantum constraints in an expansion in hBAR in more realistic theories.