  In gauge/gravity duality, points which are not causally related on the
boundary cannot be causally related through the bulk; this is the statement of
boundary causality. By the Gao-Wald theorem, the averaged null energy condition
in the bulk is sufficient to ensure this property. Here we proceed in the
converse direction: we derive a necessary as well as sufficient condition for
the preservation of boundary causality under perturbative (quantum or stringy)
corrections to the bulk. The condition that we find is a (background-dependent)
constraint on the amount by which light cones can "open" over all null bulk
geodesics. We show that this constraint is weaker than the averaged null energy
condition.
