Super-Minisuperspace and New Variables

TL;DR

This paper studies supersymmetric Bianchi type A models in supergravity using Ashtekar variables, identifying conditions for classical algebra preservation and quantizing the models to find physical states.

Contribution

It introduces a specialized approach to supergravity models with Ashtekar variables, focusing on Bianchi type A models and their quantization.

Findings

Poisson algebra preserved only for Bianchi type A models

Quantization yields physical states in triad representation

Results are formal due to lack of an inner product

Abstract

We consider the specialization to spatially homogenous solutions of the Jacobson formulation of N=1 canonical supergravity in terms of Ashtekar's new variables. We find that the classical Poisson algebra of the supersymmetry constraints is preserved by this specialization only for Bianchi type A models. The quantization of supersymmetric Bianchi type A models is carried out in the triad representation. We find the physical states of this quantum theory. Since we are missing a suitable inner product on these physical states, our results are only formal.