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created electric-magnetic duality
(and dual heterotic string theory as an example)
Presumably it would good to mention here the duaity between the M2 and M5 brane.
Is that something the p-brane story could know about?
Right, so the fact that the 4-form $G_4$ which the M2-brane couples to is to be the Hodge-dual of the 7-form $G_7$ which the M5-brane couples to
$G_7 = \star G_4$is imposed by the sugra equations of motion. This is not seen by the cocycles themselves, but comes from imposing Cartan geometry: When we go beyond speaking of the cocycles themselves and instead ask for their “definite globalization” (here) and ask that to be torsion-free, then this implies the SuGra equations of motion (here) and part of these equations is the “electric/magnetic self-duality” of the M-brane charges.
To my mind that’s where the program is headed: figure out what these cocycles are non-rationally, then M-theory ought to be the quantization of their definite globalizations. (I.e. the space of definite globalizations of these cocycles ought to make a pre-n-plectic phase space of sorts, and that’s the thing to be quantized).
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