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I recently read that the equations of motion for an classical open string naturally give rise to two boundary conditions, namely Dirichlet and Neumann boundary conditions.

(i) Could someone explain to me what do these boundary conditions physically mean, in particular for open string endpoints attached to some objects say D-branes?

(ii) Which boundary condition fixes/forces the open string to live on the brane? Which one allows open strings to move only in the free spatial dimensions of the brane?

(iii) In superstring theory, we have strings that live in 10 dimensions, in order for the theory to be Lorentz invariant. Does that mean we have to compactify 6 extra spatial dimensions? If so, how do we do that? Why do they curl up in such format?

Thank you!

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# Boundary conditions on D-Branes

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