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Can knots occur in string theory?
Perturbative strings are free to self-intersect without noticing. So even
in three dimensions, where there could topologically be knots in strings,
there are none.
Might be a different issue when looked at from another point of view, as
for instance from the currently re-fashionable cosmic string point of
view. Have a look for instance at the links Jacque Distler provides here