  Double holography plays a crucial role in recent studies of Hawking radiation
and information paradox by relating an intermediate picture, in which a
dynamical gravity living on an end-of-the-world brane is coupled to a
non-gravitational heat bath, to a much better-understood BCFT picture as well
as a bulk picture. In this paper, causal structures in generic double
holographic setups are studied. We find that the causal structure in the bulk
picture is compatible with causality in the BCFT picture, thanks to a
generalization of the Gao-Wald theorem. On the other hand, consistency with the
bulk causal structure requires the effective theory in the intermediate picture
to contain a special type of superluminal and nonlocal effect which is
significant at long range or IR. These are confirmed by both geometrical
analysis and commutators of microscopic fields. Subregion correspondences in
double holography are discussed with the knowledge of this nonlocality.
Possible fundamental origins of this nonlocality and its difference with other
types of nonlocality will also be discussed.
