Nontrivial Fermion States in Supersymmetric Minisuperspace

TL;DR

This paper explores supersymmetric minisuperspace models across Bianchi types, revealing a richer set of physical states, including nontrivial fermion states, that satisfy supersymmetry and boundary conditions.

Contribution

It demonstrates the existence of physical states with fixed even fermion number in all sectors of these models, expanding understanding of their state space.

Findings

Physical states exist in all sectors with fixed even fermion number.

A specific 4-fermion state in Bianchi IX satisfies the no-boundary condition.

Supersymmetric models have a richer manifold of physical states than previously recognized.

Abstract

In this lecture supersymmetric minisuperspace models of any Bianchi type within class A of the classification of Ellis and McCallum are considered. The algebra of the supersymmetry generators, the Lorentz generators, the diffeomorphism generators and the Hamiltonian generator is determined explicitely and found to close. Different from earlier work it is established that physical states, which are annihilated by all these generators, exist in {\it all } sectors of these models with fixed even fermion number. A state in the 4-fermion sector of the Bianchi type IX model is considered as a specific example, which satisfies the `no-boundary' condition of Hartle and Hawking. The conclusion is that supersymmetric minisuperspace models have a much richer manifold of physical states than had been recognized before.