Afonso Campos
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On page 5 of the notes (https://arxiv.org/abs/1501.00007) by Veronika Hubeny on The AdS/CFT correspondence, we find the following:
Nevertheless, already at this level we encounter several intriguing surprises. Since strings are extended objects, some spacetimes which are singular in general relativity (for instance those with a timelike singularity akin to a conical one) appear regular in string theory. Spacetime topology-changing transitions can likewise have a completely controlled, non-singular description. Moreover, the so-called 'T-duality' equates geometrically distinct spacetimes: because strings can have both momentum and winding modes around compact directions, a spacetime with a compact direction of size ##R## looks the same to strings as spacetime with the compact direction having size ##\ell_{s}^{2}/R##, which also implies that strings can’t resolve distances shorter than the string scale ##\ell_{s}##. Indeed this idea is far more general (known as mirror symmetry [11]), and exemplifies why spacetime geometry is not as fundamental as one might naively expect.
The penultimate sentence states that
A spacetime with a compact direction of size ##R## looks the same to strings as spacetime with the compact direction having size ##\ell_{s}^{2}/R##.
Why does this imply that strings can’t resolve distances shorter than the string scale ##\ell_{s}##?
Nevertheless, already at this level we encounter several intriguing surprises. Since strings are extended objects, some spacetimes which are singular in general relativity (for instance those with a timelike singularity akin to a conical one) appear regular in string theory. Spacetime topology-changing transitions can likewise have a completely controlled, non-singular description. Moreover, the so-called 'T-duality' equates geometrically distinct spacetimes: because strings can have both momentum and winding modes around compact directions, a spacetime with a compact direction of size ##R## looks the same to strings as spacetime with the compact direction having size ##\ell_{s}^{2}/R##, which also implies that strings can’t resolve distances shorter than the string scale ##\ell_{s}##. Indeed this idea is far more general (known as mirror symmetry [11]), and exemplifies why spacetime geometry is not as fundamental as one might naively expect.
The penultimate sentence states that
A spacetime with a compact direction of size ##R## looks the same to strings as spacetime with the compact direction having size ##\ell_{s}^{2}/R##.
Why does this imply that strings can’t resolve distances shorter than the string scale ##\ell_{s}##?