In string theory, open strings are attached to branes. What does "attached" mean? Do they just interact with the branes, or are they related to them in some other way?
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2$\begingroup$ Homework? Someone flagged this as homework? $\endgroup$– John RennieCommented Mar 5, 2022 at 14:51
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$\begingroup$ @JohnRennie Strange, isn't it? $\endgroup$– Арман ГаспарянCommented Mar 5, 2022 at 15:11
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2$\begingroup$ "Attached" just means that if you parametrize the endpoints of the string by $x(\tau)$ (where $\tau$ is proper time), then $x(\tau_{0}) \in W_{Brane}$ for all $\tau_{0}$, where $W_{brane}$ is the worldvolume of the brane in question. $\endgroup$– Ramiro Hum-SahCommented Mar 5, 2022 at 15:49
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1$\begingroup$ "Attach: to fasten or fix something in position, esp. in relation to something else". What is attached to D-branes is endpoints of strings. $\endgroup$– KosmCommented Mar 5, 2022 at 15:51
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1$\begingroup$ @АрманГаспарян or, you know, "attached" to the brane :) $\endgroup$– KosmCommented Mar 6, 2022 at 9:31
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1 Answer
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Attached means that the endpoint of the strings are quite literally confined to move on the brane. Strings and branes are related via dualities, look for references of S and T dualities.
The fact that we call the theory string theory is a historical accident, we should really call it brane-theory (or at least string-brane theory) since both entities are fundamental extended objects in the full non perturbative theory.
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$\begingroup$ That is, the string somehow "belongs" to the brane? $\endgroup$ Commented Mar 15, 2022 at 21:26
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1$\begingroup$ Kind of. Open strings cannot leave the brane, unless they interact and are emitted as closed strings. $\endgroup$– RexcirusCommented Mar 15, 2022 at 21:52
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1$\begingroup$ If the brane is 3D, they have other 6 dimensions (in superstring theory). $\endgroup$– RexcirusCommented Mar 15, 2022 at 22:29
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1$\begingroup$ Correct. There is nothing particular about compact dimensions, the same applies. $\endgroup$– RexcirusCommented Mar 16, 2022 at 15:53
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1$\begingroup$ These are unrelated questions, I would suggest you to have a look at A first course in string theory by Barton Zwiebach to dig deeper. $\endgroup$– RexcirusCommented Mar 16, 2022 at 16:37