Like many, I have deep conceptual difficulty understanding how an enormous amount of closed strings can become an effective classical spacetime that satisfies Einstein's equations. I appreciate that when you allow the target-space metric of the Polyakov action to fluctuate and then demand that these fluctuations leave the string world sheet Weyl-invariant, Einstein's equations miraculously appear (Polchinski, vol.1, sect 3.7). That's amazing, yes, but that doesn't seem to explain the emergence of spacetime, but merely justify its dynamics by demanding consistency with the objects that are contained within it.
Is it possible to have a world sheet formalism that doesn't fundamentally refer to the target space at all, and then have the target space emerge later as a higher level coarse-grained description or book-keeping device for exponentially complicated world sheet dynamics?
I'm trying to imagine starting with something like the 2D conformal field theory of a closed string without any reference to an ambient spacetime. This 2D conformal field theory can branch wildly into a web of enormously complicated topologies (as closed strings can). Because of this complexity, we might later create an efficient mathematical way to keep track of all these topological connections, and this might later emerge as an effective spacetime metric.
Is this making any sense? Have I just badly re-described the Polyakov action with a different world salad? Or worse?
