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I'm curious if the electric charge of the M2 brane comes from the Kaluza Klein theory. As you all know, if something is going around the circular dimension it looks like electric charge. So is this how the M2 brane gets its electric charge?

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There is no known sense in which M-theory can be viewed as the $S^1$ Kaluza-Klein reduction of a 12-dimensional theory, so there is no sense in which the charge of the M2-brane can be viewed as a Kaluza-Klein charge. Furthermore, the M2-brane is a source for the 3-form $C_3$, whereas the charged objects for a 1-form Kaluza-Klein gauge field should be particles (i.e. objects with a 1-dimensional worldline).

The closest true statement to what you're suggesting is that the Kaluza-Klein modes of M-theory compactified on $S^1$ can be identified with the D$0$-branes in Type IIA string theory.

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  • $\begingroup$ I asked physicist David Berman, and he said that there is a Kaluza Klein interpretation of the M2 and M5 charges... Is it right? $\endgroup$ – user164839 Aug 23 '18 at 14:49
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    $\begingroup$ Perhaps he is talking about some kind of interpretation as Kaluza-Klein monopoles within the framework of exceptional field theory; this paper might be relevant - arxiv.org/abs/1409.6314 . $\endgroup$ – Mtheorist Sep 21 '18 at 11:23

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