Diagonal quantum Bianchi type IX models in N=1 supergravity

TL;DR

This paper explores quantum supergravity models with Bianchi IX symmetry, constructing wave functions that satisfy all constraints and identifying specific quantum states like Hartle-Hawking and wormhole states.

Contribution

It provides the first explicit construction of wave functions solving all quantum constraints in N=1 supergravity Bianchi IX models.

Findings

Hartle-Hawking state exists in Bianchi IX supergravity models

Wormhole state is also found in middle fermion levels

Wave functions satisfy Lorentz and supersymmetry constraints

Abstract

We take the general quantum constraints of N=1 supergravity in the special case of a Bianchi metric, with gravitino fields constant in the invariant basis. We construct the most general possible wave function which solves the Lorentz constraints and study the supersymmetry constraints in the Bianchi Class A Models. For the Bianchi-IX cases, both the Hartle-Hawking state and wormhole state are found to exist in the middle fermion levels.