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There seems to be two main boundary conditions for Strings. 1. Neumann Condition: Ends of Strings are free to move up or down. 2. Dirichlet Condition: Ends of Strings are fixed.

What other boundary conditions are there for Strings? Can anyone name all the boundary conditions we have for strings?

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closed as too broad by John Rennie, user36790, Kyle Kanos, AccidentalFourierTransform, Gert Apr 3 '16 at 2:36

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ You can mix-and-match Neumann and Dirichlet (i.e. choose Neumann in half the directions, Dirichlet in the others), but what reason do you have to believe any other boundary conditions are used? $\endgroup$ – ACuriousMind Mar 30 '16 at 11:48
  • $\begingroup$ This appears to be a list-based question. $\endgroup$ – Kyle Kanos Mar 31 '16 at 10:25
  • $\begingroup$ @KyleKanos: Uh, yes, the answer is a list of the two things already mentioned in the question. That's not too broad - neither are "good answers too long" or are there "too many possible answers". If anything, the question is unclear because there's no reason to think there are other boundary conditions in string theory. $\endgroup$ – ACuriousMind Mar 31 '16 at 11:41
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    $\begingroup$ @ACuriousMind I'm going to go out on a limb here and assume the "string theory" in this question is about a literal piece of string. $\endgroup$ – user10851 Mar 31 '16 at 22:30
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There are no other boundary conditions for (open bosonic) strings: The string is fixed in some directions and free in others. There is one important generalization though:

If you impose Dirichlet or Neumann boundary conditions for each coordinate separately, the ends of the strings will always be confined to affine subspaces of $\mathbb R^n$. But in general, the end of an open string can be confined to any $(p+1)$ dimensional submanifold, called a Dp-Brane. Dp-Branes are extremely important objects in string theory, their significance will probably later become clear in your lecture/book.

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