Quantization of the Bianchi type-IX model in supergravity

Diagonal Bianchi type-IX models are studied in quantum supergravity. The quantum constraints imply that a physical wave function has only two components: one proportional to $\exp \mathrm{}(-I)\mathrm{}$ and the other to $\exp \mathrm{}\left(I\right)\mathrm{}$, for a certain action functional $I$. General solutions to the Wheeler-DeWitt equation or to a corresponding Dirac square-root equation are not permitted. It is shown that $\exp \mathrm{}(-I)\mathrm{}$ gives the wormhole ground state. However, most strangely, there is no Hartle-Hawking state among the solutions.