Dilaton Supergravity

Some important aspects of the well-known problem of quantizing gravity appear to be mitigated in the extension of supergravity. There beside the quantum particle of usual Einstein gravity, the graviton, an additional fermionic partner, the gravitino, is introduced. Within a very powerful new approach to the simplified case of spherically (or otherwise: toroidally for gravity radiation etc.) reduced two-dimensional gravity also a promising mathematical technique to deal with general two dimensional supergravity theories has been found. The aim of the project is to elaborate problems which, thank to the very reduced (minimal) number of participating fields, can be studied here more easily, being obscured otherwise in usual approaches.

In this project the combination of the principles of quantum mechanics and of gravitation were studied in models with an additional symmetry, so-called supersymmetry, which plays an important role in modern theoretical physics, especially superstring theory. As this task cannot be solved in a satisfactory way within the full complexity of four-dimensional general relativity till this day, we considered a class of simplified models, namely dilaton supergravity in two (one time and one space) dimensions. The special ansatz to tackle this problem within this project was the reformulation of these theories in terms of so- called graded Poisson-Sigma models, a strategy that had proven its particular advantages at hand of simpler models of gravity in the past already. In this way many new and exact results on two-dimensional dilaton supergravity could be derived, which in paricular led to interesting insights into the quantum dynamics of supergravity that are important for the four (or higher) dimensional case as well. As the graded Poisson-Sigma models are a very general concept we had to identify as a first step a class of those models that actually describe two-dimensional dilaton supergravity. Having done so we could prove the equivalence of these models with known two-dimensional dilaton supergravity theories formulated formulated in the so-called superspace. This ensured that all our results are also valid for this very familiar class of dilaton supergravities. In this way we could derive the complete classical solution and, in a second step, the exact non- perturbative quantization thereof. More interesting results can be obtained if instead of pure gravity the coupling of matter fields (of dynamical particles) is considered. Thanks to our identification this was a relatively easy task. The quantization procedure is much more complicated now, but it turned out to be feasable. In this way we could calculate the quantum-interaction of matter and gravitational background, as it could e.g. be seen in a future collider with very high energies, within our simplified models. The main results from earlier calculations with non- supersymmetric models were confirmed, at the same time a much richer structure of interactions due to supersymmetry was found. In a next step we showed that it is possible to generalize this program to extended supergravity (more than one supersymmetries), which is important as these models are much closer to four- dimensional supergravity. Another direction of our investigations considered space-times with explicit boundaries. Here we could show important modifications if the boundary is considered to be a horizon (the "surface" of a black hole for an outside spectator). Though horizons are not real boundaries of space-time, such idealizations are important to gain insights into the microscopical nature of (quantum-)black-holes.