The Hartle-Hawking state for the Bianchi IX model in supergravity

Abstract

We solve the quantum constraints for homogeneous N=1 supergravity on 3-geometries with a Bianchi IX metric. Because these geometries admit Killing vectors with the same commutation relations as the angular momentum generators, there are two distinct definitions of homogeneity. The first of these is well-known and has been shown by D'Eath to give the wormhole state. We show that the alternative definition of homogeneity leads to the Hartle-Hawking ``no boundary" state.