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Taking into account the higher spin theories, from which string theory is an effective field theory, I just wondering if there is something to do to extend supersymmetry to any dimension without any mathematical consistency failure. Could string-theory/M-theory be formulated in such a way fields of ANY spin naturally occur? After all, we have F-theory or S-theory in 12D and 13D.

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    $\begingroup$ The Nahm classification, c.f. math.ucr.edu/home/baez/week158.html , implies by elementary arguments $D = 11$ is the maximum dimension $\endgroup$ – bolbteppa Jan 25 '18 at 19:47
  • $\begingroup$ Some people do consider theories with more supersymmetries, e.g., Toppan in his papers... $\endgroup$ – riemannium Jan 25 '18 at 20:14
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    $\begingroup$ Sure but then, from that link, you have to drop "the reasonable assumption that there be no massless particles with spins greater than two" and this is not a good idea apparently because "there's a paper by Witten in the above book that contains references to papers that supposedly explain why particles of spin > 2 are bad" :p $\endgroup$ – bolbteppa Jan 25 '18 at 20:37
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    $\begingroup$ To be fair, there is study of higher spin theories, so "spin > 2 are bad" is not taken as seriously as it used to be. $\endgroup$ – AHusain Jan 25 '18 at 23:55
  • $\begingroup$ Related to this question $\endgroup$ – Nogueira Jan 26 '18 at 18:51
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The papers https://arxiv.org/abs/1409.2476 and https://arxiv.org/abs/1504.00602 by Choi discuss supergravity in twelve dimensions.

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  • $\begingroup$ Note that Choi considers one dimension compactified from the start, cf. the abstract: "This condition prevents us from violating the condition on the maximal number of real supercharges, which should be thirty-two." In other words, the amount of SUSY is just as in eleven dimensions. $\endgroup$ – Toffomat Mar 24 at 12:55

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