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Super Cartan geometry, LQG and applications

Nov 09
Group Seminar
2:00 pm o'clock to 3:30 pm o'clock
Konstantin Eder (FAU Erlangen-Nürnberg)

This talk is devoted to the geometric approach to supergravity and applications in Lopp Quantum Gravity (LQG). We interpret supergravity in terms of a super Cartan geometry and 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 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. We will sketch the quantization of the chiral theory making use of the enlarged gauge symmetry and encounter various similarities with the standard quantization scheme of fermions in LQG. As an application, we study a class of symmetry reduced models of chiral supergravity. There, the enlarged gauge symmetry turns out to be 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.