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The picture of wiki showed some strings attached on D-branes. However, consider those D2 branes in 3 dimensional world. Then D2 branes had two "sides".

Case 1. Let a string started at one of such D2 brain(A) on the up side(U) and ended at the down side(D). Would it be a different particle than that of a photon i.e. a string started from AU and ended on AU?

Case 2. What if there's a different D2 brain(B), does the particle start from AU and end on BU the same as a particle start from AU and end on BD?

Case 3. What if the string started on AU and ended on AU, but such that the start point and end point was the same? Was such string an open string or a closed string? What kind of particle was it?

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This question can be answered at two levels.

The physics is the same on both "sides" in the cases you're asking for.

The physics at "both sides" of a D-brane may differ dramatically in the general case.

Example 1 (the dramatic one): In page 9 of Orientifold Precis is dicussed the existence of an stable but non-BPS 8-brane that can serve as a domain wall separating type IIA superstring theory in ten dimensions and his IIB counterpart (also in ten dimensions) by a finite distance.

Example 2 (the case with defects): The spacetime of type $I^{´}$ superstring theory has a topology given by $\mathbb{R}^{9} \times [0,\pi R]$ where $R\in \mathbb{R}$ and $[0,\pi R]$ is an interval. Two orientifold 8-planes are located at $\mathbb{R}^{9} \times \{0\}$ and $\mathbb{R}^{9} \times \{\pi R\}$. Now, consistency require to add 32 D8- branes at fixed fixed positions on the interval, those branes can serve as boundary conditions for type $I^{´}$ strings and it is pretty clear that the physics changes if you are at the side of a D-brane or at the immediate side of an orientifold plane.

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