Supersymmetric minisuperspace with non-vanishing fermion number

TL;DR

This paper explores supersymmetric minisuperspace models derived from N=1 supergravity, revealing the existence of infinitely many physical states with non-zero fermion number, thus expanding their potential usefulness.

Contribution

It demonstrates that minisuperspace models in supergravity can have a rich spectrum of physical states, including those with non-vanishing fermion number, unlike previous assumptions.

Findings

Existence of infinitely many physical states with non-zero fermion number

Closure of the supersymmetry, Lorentz, diffeomorphism, and Hamiltonian algebras

Validation of minisuperspace models in supergravity as useful tools

Abstract

The Lagrangean of $N=1$ supergravity is dimensionally reduced to one (time-like) dimension assuming spatial homogeneity of any Bianchi type within class A of the classification of Ellis and McCallum. The algebra of the supersymmetry generators, the Lorentz generators, the diffeomorphism generators and the Hamiltonian generator is determined and found to close. In contrast to earlier work, infinitely many physical states with non-vanishing even fermion number are found to exist in these models, indicating that minisuperspace models in supergravity may be just as useful as in pure gravity.