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This is 1 of the great unknowns in physics. General Relativity postulates that gravity is a curvature of spacetime created by mass, but it does not explain how that curvature occurs.
As Vern said, quantum physics has the graviton - a particle that carries the force of gravity in the same way that a photon carries electromagnetism.
Yup, but the problem with QM's graviton is that it really just shifts the problem down a few levels and still eventually ends up with an abstract "and thus is gravity actioned". Just as relativity doesn't give the mechanism whereby matter curves space-time, QM doesn't say exactly what a graviton does except in terms of other QM abstracts; exactly how does the graviton carry/mediate the force of gravity, and exactly what is the nature of this force of gravity that is being carried/mediated? We're back to the original question again, without really getting anywhere.
If one thinks about the basic particles of matter as invisible little spheres which possess an invariable speed of light, then all interactions of matter like states and electrodynamic phenomena can be described and thus we would have erected the bridge between the material and immaterial world that Mr. Planck wanted.
More straight forwardly, there's T duality which requires circular dimensions. The state of a string is defined by its momentum (which comes in quantized chunks if you're on a periodic space) and its winding number, which is the number of times it wraps the circular dimension (obviously). This is a purely 'stringy' effect because you can't use points to wrap things. If you have a look on the Wiki page for T duality you'll see equations involving these momentum and winding numbers and the page explains how the non-zero winding numbers allow for the duality. Without this non-trivial you wouldn't have winding numbers.
Strings and spacetime geometry The classical theory of spacetime geometry that we call gravity consists of the Einstein equation, which relates the curvature of spacetime to the distribution of matter and energy in spacetime. But how do the Einstein equations come out of string theory? If a closed string is traveling in a curved spacetime, then the coordinates of the string in spacetime feel this curvature as the string propagates. Once again, the answer lies on the string worldsheet. In order for their to be a consistent quantum theory in this case, the curved space in which the string travels must be a solution to the Einstein equations. Now this is really something! This was a very convincing result for string theorists. Not only does string theory predict the graviton from flat spacetime physics alone, but string theory also predicts the Einstein equation will be obeyed by a curved spacetime in which strings propagate.