Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models

TL;DR

This paper develops a spin foam quantization method for super BF theories, specifically applying it to 3D supergravity with fermionic degrees of freedom, advancing the understanding of quantum supergravity models.

Contribution

It introduces a super spin foam model for super BF theory, including a super-Ponzano-Regge model with fermionic degrees of freedom, and discusses both path integral and canonical quantization approaches.

Findings

Exact quantization of 3D supergravity (p=1,q=1)

Construction of super-Ponzano-Regge model with OSp(1|2) gauge group

Proposal for incorporating fermionic degrees of freedom in spin foam models

Abstract

We show how super BF theory in any dimension can be quantized as a spin foam model, generalizing the situation for ordinary BF theory. This is a first step toward quantizing supergravity theories. We investigate in particular 3-dimensional (p=1,q=1) supergravity which we quantize exactly. We obtain a super-Ponzano-Regge model with gauge group OSp(1|2). A main motivation for our approach is the implementation of fermionic degrees of freedom in spin foam models. Indeed, we propose a description of the fermionic degrees of freedom in our model. Complementing the path integral approach we also discuss aspects of a canonical quantization in the spirit of loop quantum gravity. Finally, we comment on 2+1-dimensional quantum supergravity and the inclusion of a cosmological constant.