Supersymmetric Spin Networks and Quantum Supergravity

TL;DR

This paper introduces supersymmetric spin networks as gauge invariant states for supergravity, analyzing the Osp(1/2) case, and extends quantum geometry operators with a discrete spectrum.

Contribution

It defines supersymmetric spin networks and applies them to non-perturbative supergravity quantization, extending quantum geometry tools to supersymmetric theories.

Findings

Supersymmetric spin networks form a complete gauge invariant basis.

The supersymmetric area operator has a discrete spectrum.

The spectrum can distinguish supergravity from quantum general relativity.

Abstract

We define supersymmetric spin networks, which provide a complete set of gauge invariant states for supergravity and supersymmetric gauge theories. The particular case of Osp(1/2) is studied in detail and applied to the non-perturbative quantization of supergravity. The supersymmetric extension of the area operator is defined and partly diagonalized. The spectrum is discrete as in quantum general relativity, and the two cases could be distinguished by measurements of quantum geometry.