Three-dimensional Quantum Supergravity and Supersymmetric 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.