Super Cartan geometry and (loop) quantum supergravity

Abstract: 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.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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