Quantum states on supersymmetric minisuperspace with a cosmological constant

TL;DR

This paper explores quantum states in supersymmetric minisuperspace models with a cosmological constant, providing exact solutions using Chern-Simons theory and analyzing their properties in different variables.

Contribution

It presents new exact solutions to supersymmetry and Lorentz constraints in quantum supergravity with a cosmological constant, including explicit forms and integral representations.

Findings

Exact solutions in Ashketar variables with reality conditions

Integral solutions in tetrad-representation with different contours

Recovery of earlier solutions in the zero cosmological constant limit

Abstract

Spatially homogeneous models in quantum supergravity with a nonvanishing cosmological constant are studied. A class of exact nontrivial solutions of the supersymmetry and Lorentz constraints is obtained in terms of the Chern-Simons action on the spatially homogeneous 3-manifold, both in Ashketar variables where the solution is explicit up to reality conditions, and, more concretely, in the tetrad-representation, where the solutions are given as integral representations differing only by the contours of integration. In the limit of a vanishing cosmological constant earlier exact solutions for Bianchi type IX models in the tetrad-representation are recovered and additional asymmetric solutions are found.