Super Cartan geometry, loop quantum supergravity and applications
This talk is devoted to the geometric approach to supergravity and applications in the framework of loop quantum gravity. Among other things, this approach leads to a reformulation of the theory in which (part of) supersymmetry manifests itself in terms of a gauge symmetry. Using the interpretation of supergravity in terms of a super Cartan geometry, we will derive the Holst variant of the MacDowell-Mansouri action for N=1 and N=2 AdS supergravity in D=4 for arbitrary Barbero-Immirzi parameters. We will show that these actions provide unique boundary terms that ensure local supersymmetry invariance at boundaries. The chiral case is special. The action is invariant under an enlarged gauge symmetry, and the boundary theory is a super Chern-Simons theory. The action also implies boundary conditions that link the super electric flux through, and the super curvature on, the boundary. Applications we have in mind are supersymmetric black holes and loop quantum cosmology. To this end, we will study a class of symmetry reduced models of chiral supergravity. The enlarged gauge symmetry of the chiral theory is essential as it allows for nontrivial fermionic degrees of freedom even if one imposes spatial isotropy. The quantization of the theory yields a natural state space and allows a consistent implementation of the constraint algebra.
Finally, we will give an outlook on applications towards a quantum description of supersymmetric black holes in the context of LQG and possible relations to superstring theory.