Exact Results in Chern-Simons Supergravity
P. Valtancoli

TL;DR
This paper develops an exact non-perturbative method for solving Chern-Simons supergravity with point particles, extending previous gravity techniques to include supersymmetry and deriving explicit solutions for the two-body case.
Contribution
It introduces a superanalytic mapping approach to solve the interacting supergravity N-body problem exactly, extending existing gravity methods to supersymmetric cases.
Findings
Exact two-body supergravity solutions derived.
Superanalytic mappings constructed explicitly.
Fermionic geodesic equations defined via non-perturbative divergence cancellation.
Abstract
We propose an extension of a recent non-perturbative method suited for solving the N-body problem in (2+1)-gravity to the case of Chern-Simons supergravity. Coupling with supersymmetric point particles is obtained implicitly by extending the DJH matching conditions of gravity. The consistent solution of the interacting case is obtained by building a general non-trivial mapping, extending the superanalytic mapping, between a flat polydromic supercoordinate system and a physical one , representing the DJH matching conditions around the superparticles. We show how to construct such a mapping in terms of analytic functions, and we give their exact expressions for the two body case. The extension to the N body case is also discussed. In the Minkoskian coordinates the superparticles move freely, and in particular the fermionic coordinates are constants, whose…
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