Quantization of a Locally Supersymmetric Friedmann Model with Supermatter

TL;DR

This paper develops a quantum cosmological model incorporating local supersymmetry and supermatter, deriving the supersymmetry constraints and solutions for specific geometries, revealing limitations on wormhole states.

Contribution

It introduces a canonical quantization framework for N=1 supergravity with supermatter in a Friedmann minisuperspace, analyzing quantum states with different Kähler geometries.

Findings

Derived supersymmetry and gauge constraints for the model.

Solved quantum state equations for specific geometries.

Found that certain geometries permit Hartle-Hawking states but not wormhole states.

Abstract

The general theory of N = 1 supergravity with supermatter is studied using a canonical approach. The supersymmetry and gauge constraint generators are found. The framework is applied to the study of a Friedmann minisuperspace model. We consider a Friedmann k = + 1 geometry and a family of spin-0 as well as spin-1 gauge fields together with their odd (anti-commuting) spin-1/2 partners. The quantum supersymmetry constraints give rise to a set of first-order coupled partial differential equations for the components of the wave function. As an intermediate stage in this project, we put both the spin-1 field and its fermionic partner equal to zero. The physical states of our simplified model correspond effectively to those of a mini-superspace quantum cosmological model possessing N=4 local supersymmetry coupled to complex scalars with spin-1/2 partners. The different supermatter models are given by specifying a K\"ahler metric for the scalars; the allowed quantum states then depend on the K\"ahler geometries. For the cases of spherically symmetric and flat K\"ahler geometries we find the general solution for the quantum state with a very simple form. However, although they allow a Hartle-Hawking state, they do not allow a wormhole state.