What is the underlying connection between geometry and matter in string theory?

[Adrian59]

2. to understand how the combined geometry-and-matter entity arises
(why geometry responds to matter and why matter follows geometry, they must be fundamentally the same underlying thing because of this close interaction, what is this thing?)

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You have posed what I would agree is a fundamental question. One could say that Einstein’s great leap of imagination was to recognise because of the equivalence of inertial mass with gravitational mass that mass was warping space. However, to my interpretation the surprise is that this works. Einstein assumed that matter warping space created gravity & derived his general theory of relativity from this assumption so the surprise is that it works so well without a clear understanding why. As you said, Marcus, it’s this relationship between the geometry of space-time & matter that needs an explanation.