Physical States in d=3,N=2 Supergravity

Details Physical States in d=3,N=2 Supergravity Physical States in d=3,N=2 Supergravity

1993-09-09

arxiv.org/abs/gr-qc/9309006v1

Phys.Lett. B318 (1993) 115-121

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, Report DESY 93-125, THU-93/19

Scientific paper

10.1016/0370-2693(93)91793-M

To clarify some issues raised by D'Eath's recent proposal for the physical states of $N=1$ supergravity in four dimensions, we study pure (topological) $N=2$ supergravity in three dimensions, which is formally very similar, but much easier to solve. The wave functionals solving the quantum constraints can be understood in terms of arbitrary functions 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.

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