I am currently reading Polchinski page 81, and am not 100% clear with the explanation given regarding why any open string theory necessarily contains closed strings. It is stated, quoted from page 81:

Consider the interactions in figures 3.4(a) and (b), but time reversed: respectively two open strings joining into one, and an open to closed string transition. Near the interaction point these are the same, two endpoints coalescing. To have the first interaction without the second would require some nonlocal constraint on the dynamics of the string; this would surely be inconsistent. One can make the same argument with figures 3.4(c) and (d), where the interaction is locally the reconnection of a pair of strings. So if any open string interaction is allowed, then so is some process in which closed strings are produced from open strings.

He also gives an argument in the paragraph above which I don't quite understand. In particular, in this case, why exactly would having the first interaction without the second require a nonlocal constraint and why would this be inconsistent?

Could someone please explain in more detail the explanations from these two paragraphs?


You have two string ends coming together, in either case. The ends joining don't know if they are two separate open strings, or if they are joined at the other end. the only way the string would "know" would be some sort of non-locality that tells two ends, before they join, if they are already joined at the other end.

Why would this be inconsistent? That's generally how non-locality works.

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