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arXiv · 0710.3540

N=2 supersymmetric spin foams in three dimensions

Etera R. Livine·James P. Ryan
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Abstract

We construct the spin foam model for N=2 supergravity in three dimensions. Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has representations which are not completely reducible. This complicates the procedure when building a state sum. Fortunately, one can and should excise these representations. We show that the restricted subset of representations form a subcategory closed under tensor product. The resulting state-sum is once again a topological invariant. Furthermore, within this framework one can identify positively and negatively charged fermions propagating on the spin foam. These results on osp(2|2) representations and intertwiners apply more generally to spin network states for N=2 loop quantum supergravity (in 3+1 dimensions) where it allows to define a notion of BPS states.

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Etera R. Livine, James P. Ryan. 2007-10-18. N=2 supersymmetric spin foams in three dimensions. https://doi.org/10.1088/0264-9381%2F25%2F17%2F175014

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