A successful approach in understanding the holographic phenomena has been the asymptotic symmetry analysis. For example, the Kerr-CFT and similar soft hair proposals claim to count the microstates of black holes. Recent interest in asymptotic symmetries in flat space is largely due to the discovery of the relation between soft photon/ graviton theorems, asymptotic symmetries, and memory effects. This lead to a symmetry interpretation of soft theorems which were by then understood as Feynman diagrammatic identities.
The study of asymptotic symmetries in anti de Sitter space is older and is well understood. AdS space is not globally hyperbolic and boundary fields are most often fixed as Dirichlet conditions. For this reason, the asymptotic symmetries are trivial in the standard boundary conditions of gauge theories, which are also advocated in AdS/CFT correspondence. Nevertheless, the question is whether there exist mixed boundary conditions which allow infinite dimensional asymptotic symmetries for gravity and gauge theories in anti de sitter space.
In the conceptual side, the holographic understanding of the new conserved charges deserves attention. The obvious meaning of a Neumann boundary condition for gravity is the existence of gravity on the boundary.
A significant example is 2-form theory which is an essential sector of supergravity in AdS. It has been shown that p-forms admit non-trivial ASG in at space. If that is the case in anti de Sitter as well, it is much interesting to
figure out the holographic meaning of the result as a global symmetry of the dual theory.
These analyses can bridge the conceptual and technical gap between flat and AdS studies which is quite important in holography.