Globality of Heaven-on-Earth AdS fillings and their holographic interpretation

Establish whether the self-dual bulk AdS$_4$ metrics generated by the Heaven-on-Earth construction are globally well-defined under appropriate assumptions, and clarify their relationship with bulk fillings arising in conventional holography.

Background

The paper identifies the bulk twistor space of a self-dual asymptotically AdS$_4$ spacetime with the ambitwistor space of its conformal boundary using LeBrun’s Heaven-on-Earth construction. The explicit analysis is carried out for a conformally flat boundary and the Poincaré patch.

The authors note that the construction does not automatically guarantee a global self-dual AdS$_4$ filling and that it is unclear how such fillings relate to those used in conventional holography. Resolving this issue is necessary for extending the local ambitwistor description to globally meaningful holographic spacetimes.