The static-patch partition function of three-dimensional de Sitter gravity is identified with the future-boundary wavefunction, giving a dense discrete spectrum with negative degeneracies.
Notes on the (2+1)-Dimensional Wheeler-DeWitt Equation
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abstract
In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of information about solutions and their interpretation. In particular, strong evidence is presented that Wheeler-DeWitt quantization is not equivalent to reduced phase space quantization.
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The spectrum of pure dS$_3$ gravity in the static patch
The static-patch partition function of three-dimensional de Sitter gravity is identified with the future-boundary wavefunction, giving a dense discrete spectrum with negative degeneracies.