Exact Results in Quantum Theory & Gravity

The first part of the talk will be a brief introduction to conformal tractor calculus, and to the construction of conformal structures associated with maximally non-integrable vector distributions on 5-manifolds. In the second part, I will report on joint work with Travis Willse on the geometry of such conformal structures admitting parallel standard tractors: A parallel standard tractor determines a partition of the manifold into several submanifolds, each naturally endowed with a geometric structure. This reveals links between (2,3,5) distributions and several other geometries, including, Sasaki-Einstein structures of signature (2,3), Fefferman-conformal structures, and their para-complex analogues.