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Source: Brian Greene's Elegant Universe

1)

I finally understand why string theory is a theory of quantum gravity after reading chapter 6 - the quantum fluctuations/foam that made a mess of the smooth structure of spacetime is not an issue, it was an artificial of calculated where the fundamental building blocks of the universe where infinitesimal with no “thickness.”

But why strings? Why don’t non-infinitesimal spheres work?

On page 157 and 158, Greene mentions Pauli, Heisenberg, Dirac, and Feynman all trying this (no strings just trying non-point particles) and failing. Can I have some references to look into to understand why they failed?

Greene mentions that the vibrational property of strings enables gravitons to come into the picture, thus bringing gravity into the theory (page 165). Can someone explain how the construction of a messenger particle in a theory implies the corresponding forces in the theory?

2)

In regards to the string coupling constant, Greene says on page 295, “What is the value of the string coupling constant (or, more precisely, what are the values of the string coupling constants in each of the five string theories)? At present, no one has been able to answer this question.” Yet in the 20 or so pages that follow, the perturbations methods of string theory are introduced, notably dualities.

My confusion lies in how to reconcile the aforementioned quote with ones like “... so long as the string coupling constant stays in the perturbative realm” (304). If we can tell when the coupling constant is in the perturbative regime, how is it that no one knows what the string coupling constants is for some/all of the five string theories?

If it is indeed the case that the string coupling constant is still an open problem, could vertex operator algebras be a fruitful approach to the problem? See Lepowsky’s explanation (https://arxiv.org/abs/0706.4072) of using VOAs in string theory here:

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