Europe/Lisbon
Room P3.10, Mathematics Building — Online

Konstantin Eder, University of Erlangen–Nürnberg
Super Cartan geometry and (loop) quantum supergravity

In this talk, a mathematically rigorous approach toward geometric supergravity will be discussed which, in the physical literature, is usually known as the Castellani-D'Auria-Fré approach. To this end, using tools from supergeometry, the notion of a super Cartan geometry will be introduced. Interestingly, in order to consistently incorporate the anticommutative nature of fermionic fields, the ordinary category of supermanifolds needs to be generalized in a physically consistent way leading to the notion of so-called enriched supermanifolds. We then apply this formalism to discuss a geometric formulation of (generalized) pure Anti-de Sitter supergravity with N=1,2 supersymmetry in D=4 modified by an additional Holst term. In this context, we will also talk about so-called picture changing operators (PCO) and how they can be implemented in a mathematically rigorous way. Finally, an outlook will be given for applications of this formalism to (loop) quantum supergravity and the description of quantum supersymmetric black holes.

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Konstantin's slides.

Local participants are invited to join us in room 3.10 (3rd floor, Mathematics Department, Instituto Superior Técnico).