I would like to understand how Physicists think of space-time in the context of String Theory. I understand that there are $3$ large space dimensions, a time dimension, and $6$ or $7$ (or $22$) extra dimensions, and all these dimensions need to fit together in a way such that the extra dimensions are compactified (with a Calabi-Yau or $G_2$ structure).
My question, however is not about the possible $10$, $11$ or $26$ dimensional manifolds that may be possible, but about whether string theorists consider space-time as somehow quantized (or discrete), or rather as a continuous manifold, or are both options possible? In other words, can strings move continuously through space, or are there a discrete set of locations where strings can be, and does string theory rule out one of the options?
How about the same question in loop quantum gravity (LQG)? Should I think of the spin networks in LQG as describing a discrete space-time?
Thanks for your insight, or any references you may be able to provide!
Best Answer
I think Anna s comment is correct, in LQG spacetime consists of discrete atoms and in ST it is continuous.
In addition, This article contains an interesting and quite accessible Nima talk related to the topic. Therein Nima explains why the present notions of spacetime are doomed and introduces the recent cutting edge ideas about how spacetime could emerge from a newly discovered and not yet fully explored structure called T-theory.