In string theory, we have a fundamental length $l_s$. From T-duality, we expect a duality between UV and IR; a length smaller than $l_s$ is regarded as a length greater than $l_s$. We do not see any length scale smaller than $l_s$. From UV completeness, string theory is well-defined in arbitrary high energy and cannot be an effective theory.

Does this contradict to the existence of the string length? For example, if you probe our spacetime smaller than $l_s$, you must “see” a string and string theory could break down. It seems contradictory to UV completeness.

Furthermore, we cannot neglect the finite size effect of $l_s$, so string theory should be treated nonperturbatively. But even in nonperturbative string theory, the spacetime should be discrete in unit of $l_s$ and there seems to be a UV cutoff (cf. spacetime cannot be continuous) if the closed strings give rise to gravitons even in nonperturbative string theory.

To summarize, my question is “Although there is a fundamental length $l_s$ present, how can string theory is UV-complete beyond $l_s$?”



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