general relativity - How does classical GR concept of space-time emerge from string theory?

First, I'll state some background that lead me to the question.

I was thinking about quantization of space-time on and off for a long time but I never really looked into it any deeper (mainly because I am not yet quite fluent in string theory). But the recent discussion about propagation of information in space-time got me thinking about the topic again. Combined with the fact that it has been more or less decided that we should also ask graduate level questions here, I decided I should give it a go.

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So, first some of my (certainly very naive) thoughts.

It's no problem to quantize gravitational waves on a curved background. They don't differ much from any other particles we know. But what if we want the background itself to change in response to movement of the matter and quantize these processes? Then I would imagine that space-time itself is built from tiny particles (call them space-timeons) that interact by means of exchanging gravitons. I drawed this conclusion from an analogy with how solid matter is built from atoms in a lattice and interact by means of exchanging phonons.

Now, I am aware that the above picture is completely naive but I think it must in some sense also be correct. That is, if there exists any reasonable notion of quantum gravity, it has to look something like that (at least on the level of QFT).

So, having come this far I decided I should not stop. So let's move one step further and assume string theory is correct description of the nature. Then all the particles above are actually strings. So I decided that space-time must probably arise as condensation of huge number of strings. Now does this make any sense at all? To make it more precise (and also to ask something in case it doesn't make a sense), I have two questions:

1. 
   

   In what way does the classical space-time arise as a limit in the string theory? Try to give a clear, conceptual description of this process. I don't mind some equations, but I want mainly ideas.

   
   


2. 
   

   Is there a good introduction into this subject? If so, what is it? If not, where else can I learn about this stuff?

   
   

Regarding 2., I would prefer something not too advanced. But to give you an idea of what kind of literature might be appropriate for my level: I already now something about classical strings, how to quantize them (in different quantization schemes) and some bits about the role of CFT on the worldsheets. Also I have a qualitative overview of different types of string theories and also a little quantitative knowledge about moduli spaces of Calabi-Yau manifolds and their properties.

Answer

First, you are right in that non-Minkowski solutions to string theory, in which the gravitational field is macroscopic, it should be thought of as a condensate of a huge number of gravitons (which are one of the spacetime particles associated to a degree of freedom of the string). (Aside: a point particle, corresponding to quantum field theory, has no internal degrees of freedom; the different particles come simply from different labels attached to ponits. A string has many degrees of freedom, each of which corresponds to a particle in the spacetime interpretation of string theory, i.e. the effective field theory.)

To your question (1): certainly there is no great organizing principle of string theory (yet). One practical principle is that the 2-dimensional (quantum) field theory which describes the fluctuations of the string worldsheet should be conformal, i.e. independent of local scale invariance of the metric. This allows us to integrate over all metrics on Riemann surfaces only up to diffeomorphisms and scalings, which is to say only up to a finite number of degrees of freedom. That's an integral we can do. (Were we able to integrate over all metrics in a way that is sensible within quantum field theory, we would already have been able to quantize gravity.) Now, scale invariance imposes constraints on the background spacetime fields used to construct the 2d action (such as the metric, which determines the energy of the map from the worldsheet of the string). These constraints reduce to Einstein's equations.

That's not a very fundamental derivation, but formulating string theory in a way which is independent of the starting point ("background independence") is notoriously tricky.

(2): This goes under the name "strings in background fields," and can be found in Volume 1 of Green, Schwarz and Witten.