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

TL;DR

This paper demonstrates how different definitions of homogeneity in Bianchi IX supergravity models lead to distinct quantum states, including the Hartle-Hawking no boundary state, expanding understanding of quantum cosmology.

Contribution

It introduces an alternative homogeneity condition in Bianchi IX supergravity that results in the Hartle-Hawking state, complementing the known wormhole state.

Findings

Different homogeneity definitions yield distinct quantum states.

The alternative homogeneity condition produces the Hartle-Hawking no boundary state.

The work connects symmetry properties with quantum cosmological solutions.

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.