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I have read that string theory predicts (or requires ?) the existence of gravitons. So, would that make it a quantum theory of gravity ?

If so, I have also read that quantum gravity would allow us to understand what happens at the singularity inside a black hole. What does string theory say about this ?

If string theory can't make any predictions about this, what are we missing ? Is the theory incomplete ? Or is it that we have multiple string theories - hence, multiple ways to quantize gravity - and don't know which is the right one ?

I'm not a physicist, so just looking for an explanation at the Brian Greene popular book level. :)

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A paper with precisely the same title as this question has appeared on the archive: arxiv.org/abs/1105.6359 –  user4085 Jun 18 '11 at 1:41
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I have read that string theory predicts (or requires ?) the existence of gravitons.

String theory models contain massless spin-2-particles called gravitons, therefore they postdict their existence. The fact that the exchange of such particles results in a GR-like gravitational force was discovered some time before string theory came into being, around 1950, and made popular by Richard Feynman in his lectures on gravitation (see amazon).

So, would that make it a quantum theory of gravity?

Classical wavelike phenomena correspond to quantum mechanical particles ("wave-particle duality"), and since GR describes waves, many people believe that a quantum version should describe gravitons. On the other hand, string theory works with a classical GR background, so that it can describe quantum corrections to a classical situation only. It is an open problem if that is already all of the story, or if a quantum theory of gravity would need to alter the concept of spacetime of classical GR on a more fundamental level.

(To be fair: string theorists know and think about this problem, too, and are working on versions of string theory that incorporate a more fundamental change to spacetime.)

If so, I have also read that quantum gravity would allow us to understand what happens at the singularity inside a black hole. What does string theory say about this?

A basic assumption is this: In a consistent theory of gravitation there should not be any singularities with respect to physically relevant phenomena, and the existence of black hole singularities in GR tell us that classical GR breaks down and should be replaced by a quantum version of gravitation. String theory does not say anything about this, because, today, all formulations of string theory assume the existence of a classical spacetime. A full theory of quantum gravity may be able to explain what happens when a black hole forms in classical GR, for example. Maybe string theory will be able to do so in some future version, but not now (see my previous comment).

If string theory can't make any predictions about this, what are we missing?

Right know there are more answers to this questions than there are heads on this planet thinking about it. The problem is that string theory starts with an unmotivated and unexplainable assumption about the nature of particles, so there is basically no guidance at all what to do when you run into problems. It's not like that you have a set of axioms derived from a well established theory, run into inconsistencies, and go back to the drawing board to see what axiom may have to be replaced...

Or is it that we have multiple string theories - hence, multiple ways to quantize gravity - and don't know which is the right one?

All string theory variants try to do the quantization of gravity the same way (exchange of gravitons on a classical background), so the existence of a bunch of different "string theories" should not be mixed up the the existence of multiple approaches to the quantization of gravity. The question if it is possible to extract the "right" string theory from the plethora of possible ones is a topic of ongoing debate. As for now, it's basically up to you what you believe.

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How about this : athome.harvard.edu/programs/sst/video/sst1_6.html . "Where before, black holes were thought to contain nothing, string theory hypothesizes that they do contain these little strings. And the strings store information in a precise way, which never "vanishes without a trace." By viewing black holes through the lens of string theory, the clash between general relativity and quantum mechanics is resolved. " Strings do interpret black holes. –  anna v Jun 5 '11 at 11:29
    
The starting point of perturbative string theory is not an "unmotivated and unexplainable assumption about the nature of particles". Instead, it's a natural variation of the perturbative description in QFT. It may be physically wrong, but it is by no means unmotivated and unexplainable. Here it helps to remember the "worldline formalism" for QFT ncatlab.org/nlab/show/worldline+formalism . If you can see this and not naturally wonder if there could be a higher dimensional worldvolume generalization of this formalism, you have to return your theoretical physics license ;-) –  Urs Schreiber Aug 5 '13 at 12:18
    
It is not true that perturbative string theory says nothing about black hole singularities, because of "the existence of a classical spacetime". Instead, it knows about all properties of such black holes that are "protected" by supersymmetry (and these are more than for plain supersymmetric back holes). This works by following a weakly coupled configuration of branes (gravity back reaction approximately turned off) as the coupling constant is turned on. All the detailed microscopic computations of BH entropy work this way ncatlab.org/nlab/show/black+holes+in+string+theory . –  Urs Schreiber Aug 5 '13 at 12:25
    
(Not to mention that via AdS/CFT supposedly properties of quantum black holes are encoded in the dynamics of a sYM CFT on an asymptotic boundary of spacetime.) –  Urs Schreiber Aug 5 '13 at 12:25
    
The distinction between "postdiction" and "prediction" is not interesting. For instance, suppose tomorrow somebody solves the mass gap problem for Yang-Mills theory. Then we won't say "QFT postdicts the mass gap of Yang-Mills", just because we knew it already from experiment and numerics. Instead we will say "QFT explains the mass gap of Yang-Mills in that it derives it from simpler axioms". And this is true also about how string theory yields gravity. –  Urs Schreiber Aug 5 '13 at 12:30
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String theories are in the forefront of particle theory at the moment because they are the only theories that can quantize gravity and at the same time allow the incorporation of the Standard Model of particle physics within the theory. The SM can be thought as an efficient mathematical description of all the data gathered up to now for particle physics, there fore any theory of everything should incorporate it in some form.

String theories are a work in progress and in wait for data that will allow determination of constants on what exactly is nature's choice. We might be lucky with the LHC to make progress on this, we might not and will need patience and decades of experiments and theoretical studies. One can study what happens in black holes using string theory models but the reason they are popular is that they pave the way to a Theory Of Everything. Or so many physicists hope.

So yes, string theories are quantum theories of gravity and include the graviton and a host of other particles that can be counted like angels on the head of a pin. :) . It is data that is needed to solidify a specific string theory model.

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@MBN: just google for string theory phenomenology -- it is a huge enterprise which does basically just that. The standard model (and its close relatives) have been identified in many vacua I believe. Problem is, they usually come with extra unobserved stuff, wrong cosmological constant, etc. I am not sure what is the current state of locating our world in the stringy vacua. You might consider asking this question, it's definitely interesting. –  Marek Jun 4 '11 at 16:16
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@MBN, current efforts are aimed at constructing a viable SUSY GUT model, that includes the Standard Model, as opposed to just the Standard Model. Here are a couple of references: arxiv.org/abs/hep-th/0512177 , arxiv.org/abs/0811.2936 , arxiv.org/abs/0905.1968 . –  stringpheno Jun 4 '11 at 19:06
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@MBN, I gave you some example constructions that contain the SM spectrum with three chiral families as part of a SUSY GUT. Computing all the coupling constants explicitly currently presents a technical challenge, mainly due to the lack of computational tools on the geometric side. Fot the most part, this is just a difficult mathematics problem that is kind of separate from string theory. Example: computing the metric on a Calabi Yau manifold in the Heterotic compactification cited above is one such problem that needs to be addressed before any questions about SM couplings are asked. –  stringpheno Jun 4 '11 at 22:03
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@MBN, Just to add, there has been some impressive quantitative progress in local F-theory models with regard to computing the Yukawa couplings in the Standard Model: arxiv.org/abs/0910.0477 –  stringpheno Jun 4 '11 at 22:15
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@MBN When people say that the SM is part of string theory they typically mean that there exist explicit string constructions reproducing the SM particle spectrum, usually as part of a SUSY GUT. This fact in itself is highly non-trivial, although computing all the couplings would take it to a whole new level. Anyway, the only textbook that I'm aware of where modern string-theoretic constructions of the Standard Model are discussed is this one: amazon.com/String-Theory-Particle-Physics-Phenomenology/dp/… . –  stringpheno Jun 5 '11 at 4:44
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