... The new picture that emerges from this duality is that of a "quantum" CY geometry. To understand what this means it is worth recalling that in a classical space of any kind each point is specified by a set of numbers, or co-ordinates. Examples of co-ordinates are the longitude and latitude of the Earth's surface. In the quantum CY space the co-ordinates are no longer simple numbers to be specified at will. Rather they obey the Heisenberg uncertainty principle, which relates the position and momentum of a quantum particle. For the quantum CY spaces of Okounkov, Reshetikhin and Vafa's dual description of topological string theory, the long-standing dream of replacing a smooth classical space with a discrete quantum substructure is thus realized. In this system the emergence of a classical geometry out of a quantum system can be clearly controlled and understood. As is shown in further work by Vafa et al., this gives an explicit and controllable picture of the Wheeler-Hawking notion of topological fluctuations - or "foam" - in space-time (Iqbal et al. 2003). The fluctuations of topology and geometry actually become the deep origin of strings. They extend rather than reduce the predictive power of the quantum theory of gravity.
Of course many challenges remain before a full theory of this kind can be realized. Chief among these is the extension of the picture from topological strings to full string theory. A possible path has been identified, however, suggesting that in string theory, as in Einstein's gravity, the distinction between forces and the space in which they act melts away.
I hadn't seen that CERN article. Thanks for linking to it.