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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2Homework? Someone flagged this as homework? – John Rennie Mar 05 '22 at 14:51
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@JohnRennie Strange, isn't it? – Арман Гаспарян Mar 05 '22 at 15:11
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2"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. – Ramiro Hum-Sah Mar 05 '22 at 15:49
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1"Attach: to fasten or fix something in position, esp. in relation to something else". What is attached to D-branes is endpoints of strings. – Kosm Mar 05 '22 at 15:51
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@RamiroHum-Sah That is, it is not just an interaction, we can say that the string "belongs" to the brane. – Арман Гаспарян Mar 05 '22 at 18:27
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1@АрманГаспарян or, you know, "attached" to the brane :) – Kosm Mar 06 '22 at 09:31
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@Kosm Well, yes, if you consider that they are attached in such a way that their separation from the brane is impossible. – Арман Гаспарян Mar 06 '22 at 11:01
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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.
Rexcirus
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1Kind of. Open strings cannot leave the brane, unless they interact and are emitted as closed strings. – Rexcirus Mar 15 '22 at 21:52
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1If the brane is 3D, they have other 6 dimensions (in superstring theory). – Rexcirus Mar 15 '22 at 22:29
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Check the picture here for more intuition: https://physics.stackexchange.com/questions/208600/is-electron-positron-annihilation-to-two-gravitons-forbidden/208797#208797 – Rexcirus Mar 15 '22 at 22:30
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That is, they are emitted into extra dimensions? What if the extra dimensions are compactified? – Арман Гаспарян Mar 16 '22 at 08:02
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1Correct. There is nothing particular about compact dimensions, the same applies. – Rexcirus Mar 16 '22 at 15:53
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And in background-independent models, where will the particles be emitted? – Арман Гаспарян Mar 16 '22 at 16:29
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1These are unrelated questions, I would suggest you to have a look at A first course in string theory by Barton Zwiebach to dig deeper. – Rexcirus Mar 16 '22 at 16:37
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Thanks. That is, for the formulation of any string theory, the existence of a background space-time is necessary? – Арман Гаспарян Mar 16 '22 at 16:45