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December, 2003 Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models
Etera R. Livine, Robert Oeckl
Adv. Theor. Math. Phys. 7(6): 951-1001 (December, 2003).

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.

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Etera R. Livine. Robert Oeckl. "Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models." Adv. Theor. Math. Phys. 7 (6) 951 - 1001, December, 2003.

Information

Published: December, 2003
First available in Project Euclid: 21 June 2004

zbMATH: 1073.83039
MathSciNet: MR2061641

Rights: Copyright © 2003 International Press of Boston

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Vol.7 • No. 6 • December, 2003
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