Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk

Understand

We study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity.

• We solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions.
• We also develop a product formula for solving these asymptotic problems in general.
• The central tools of our approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary.