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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 22nd 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated [[electric-magnetic duality]] (and [[dual heterotic string theory]] as an example)

   created electric-magnetic duality

   (and dual heterotic string theory as an example)

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 30th 2017
   • (edited Jul 30th 2017)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexPresumably it would good to mention here the duaity between the M2 and [[M5 brane]]. Is that something the [p-brane story](https://ncatlab.org/schreiber/print/StringMath2017) could know about?

   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?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 31st 2017
   • (edited Jul 31st 2017)
   • PermaLink
   Author: Urs
   Format: MarkdownItexRight, 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](https://ncatlab.org/nlab/show/definite+globalization+of+WZW+term)) and ask that to be torsion-free, then this implies the SuGra equations of motion ([here](https://ncatlab.org/nlab/show/torsion+constraints+in+supergravity#Examples11dSuGra)) 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).

   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).