Another approach is the conjectured, but yet unproven AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with anti-de Sitter asymptotics. If so, this could describe a kind of superselection sector of the putative background-independent theory. But it would still be restricted to anti-de Sitter space asymptotics, which disagrees with the current observations of our Universe. A full non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking.