Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models

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.

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Published 1 January 2003