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.

43 pages, 10 figures

References in corpus (4)

• Spin Foam Models for Quantum Gravity
• A "general boundary" formulation for quantum mechanics and quantum gravity
• Diffeomorphisms and spin foam models
• Schroedinger's cat and the clock: Lessons for quantum gravity

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• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
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• Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory
• Observables in 3d spinfoam quantum gravity with fermions
• 3d Quantum Gravity: Coarse-Graining and q-Deformation
• N=2 supersymmetric spin foams in three dimensions
• Quantum general relativity and the classification of smooth manifolds
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• The new spin foam models and quantum gravity
• Supersymmetric minisuperspace models in self-dual loop quantum cosmology
• Super Cartan geometry and the super Ashtekar connection
• $\mathcal{N}=1$ Supergravity with LQG methods and quantization of the SUSY constraint
• The particle interpretation of N = 1 supersymmetric spin foams
• The Ponzano-Regge asymptotic of the supersymmetric 6jS symbols