# Supersymmetry beyond $D=11$ spacetime dimensions

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.

• The Nahm classification, c.f. math.ucr.edu/home/baez/week158.html , implies by elementary arguments $D = 11$ is the maximum dimension – bolbteppa Jan 25 '18 at 19:47
• Some people do consider theories with more supersymmetries, e.g., Toppan in his papers... – riemannium Jan 25 '18 at 20:14
• 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 – bolbteppa Jan 25 '18 at 20:37
• 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. – AHusain Jan 25 '18 at 23:55
• Related to this question – Nogueira Jan 26 '18 at 18:51