Can Strings Always Split in String Theory?

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David Baker
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Something that's been unclear to me from the presentations I've seen of interacting string theory:

In a setting like bosonic string theory, where the interactions consist of strings splitting and joining, is it always possible for a string to split? In other words, are there "minimum-sized" strings that cannot be split further, but can only interact by joining? Or is it always possible for every string to enter into either type of interaction?

(For purposes of the question, let's say it's "possible for a string to split" if there's any non-zero amplitude at all for a split, even if splitting is extremely unlikely.)

Edit to add: References would be GREATLY appreciated!
 
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+1 to the question, and I add that I would like to see (read: to be pointed to) some actual calculation of the size of an string, specially in the fermionic case.

PS: as for the answer, my guess is that any point-size string coming out of an interaction will evolve in less than a Planck time to get a size of a Plank length. But again, it should be nice to see that explicitly.
 
Well I guess the most natural minimum size limit for a string would have to be the Planck's length...Otherwise you are getting a singularity...
At least that's the idea I got from Susskind's lecture on String and M-theory on youtube (although I haven't finished it yet)