  In a weakly coupled gravity theory in the anti-de Sitter space, local states
in the bulk are linear superpositions of Ishibashi states for a crosscap in the
dual conformal field theory. The superposition structure can be constrained
either by the microscopic causality in the bulk gravity or the bootstrap
condition in the boundary conformal field theory. We show, contrary to some
expectation, that these two conditions are not compatible to each other in the
weak gravity regime. We also present an evidence to show that bulk local states
in three dimensions are not organized by the Virasoro symmetry.
