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Journal Article

Physical states in d = 3, N = 2 supergravity


Nicolai,  Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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De Wit, B., Matschull, H.-J., & Nicolai, H. (1993). Physical states in d = 3, N = 2 supergravity. Physics Letters B, 318(1), 115-121. doi:10.1016/0370-2693(93)91793-M.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5C24-B
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 Image in more realistic theories.