Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes

The AdS/CFT conjecture in physics posits the existence of a  correspondence between gravitational theories in asymptotically Anti-de  Sitter (aAdS) spacetimes and field theories on their conformal boundary.  In this presentation, we prove rigorous mathematical statements toward  this conjecture.

In particular, we show there is a one-to-one correspondence between aAdS  solutions of the Einstein-vacuum equations and a suitable space of data  on the conformal boundary (consisting of the boundary metric and the  boundary stress-energy tensor). We also discuss consequences of this  result, as well as the main ingredient behind its proof: a unique  continuation property for wave equations on aAdS spacetimes.

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