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Firstly, General Relativity states that Spacetime is dynamic and is consonant with the distribution of matter/energy. How does String Theory predict gravity, when it is background dependent, that is it starts off with a fixed, and presumably flat space-time?
Secondly, String Theory predicts the existence of a graviton, but seeing we don't have a quantum theory of gravity, how do we even know that this is the correct quantization of gravity? In other words how do we verify that the graviton should have the properties that String theory says it does, that is what grounds do we have for believing in the properties of the graviton?
Thirdly, how do we go from the existence of gravitons to the curvature of space-time? When we talk about gravitons aren't they already existing in some space-time framework?