17/06/2014, 11:30 — 12:30 — Room P3.10, Mathematics Building
Travis Willse, The Australian National University, Canberra
Holography for parallel conformal data
The Fefferman-Graham ambient metric construction, with some technical asterisks, positively resolves the Dirichlet problem for compactification of asymptotically hyperbolic Einstein metrics, the compactification that occurs in the AdS/CFT correspondence. We show that data on the conformal boundary parallel with respect to Cartan's normal conformal connection — which is nearly the same thing as a holonomy reduction of the conformal structure — can be extended (again with an asterisk) to data parallel with respect to a natural connection on a corresponding bundle over the bulk, which in particular enables holographic study of such data. As an application, we use this extension result to construct metrics of exceptional holonomy.