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(Clickable montage of some recent posts on my instagram account that might interest you. See also the twitter and Facebook accounts. Links in sidebar.)
Hi,
Those are the two most well-known approaches, I agree. There are others. The small extra dimensions idea, as you say, is historically the one that has been most explored, and it predates the picture of being confined to a sub manifold of a large spacetime. Within string theory, compared to the niverse-as-brane idea, there are far more well-developed ideas about how various other important features (besides 3 large spatial dimensions) might arise from compactification (e.g. features of the topology of the internal spacetime imprinting as properties of the particle spectrum, like the number of families, etc. Moreover, those kinds of constructions have led to lots of rich mathematics like mirror symmetry, a web of important string dualities, and so forth. So that’s another reason they have been focussed on more. The potential phenomenology is richer.
On the other hand, since how string theory might (if it does at all) actually yield the Standard model of particle physics is still not well mapped out, there are no compelling *physics* reasons to favour one scenario over the other at this stage. We may well be surprised as to which aspects are most important in this regard.
-cvj
Dear Clifford,
Off topic question on D-branes that I hope you will answer. There are, as far as I understand, two approaches to extra dimensions in string theory. One is that they are compact and small, so we cant see them. The other is that we live on a D3 brane floating in a higher dimensional space. We are confined to the D3 brane, and that is why we perceive space to be three dimensional.
My question: is the compactification idea so popular only because it is the traditional approach invented before the discovery of d-branes? or is there clear reasons for preferring compactification over the idea of a d3 brane floating in a higer dimensional space.
Thanks for your time.