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  Is there a list of all possible Super-Poincaré algebras up to 11D and their physical supermultiplet representations?

+ 4 like - 0 dislike

From looking around it seems like there are

 - In each dimension (greater than 1, 2, or maybe 3*) essentially a finite number of possible central extensions of the Super-Poincaré algebra (of various N or (N,M) extended supersymmetry) up to continuous parameters that don't essentially change the algebra (except maybe at special values defined by at most a finite number of algebraic relationships between the central charges Edit: I realized that the lie superalgebra doesn't actually encode any information about the central charges other than that they are non-zero and commute, so any relationships betwen them would be in the representation, not the algebra, I think).
 - For each Super-Poincaré algebra with central extension a finite number of supermultiplet representations that are non-negative mass squared and do not contain spins greater than 2.

The classification of the central extensions is certainly non-trivial and because of various kinds of short multiplets the categorization of the physically relevant irreducible supermultiplets is possibly non-tivial.

It seems that because of the eccentricities of lower dimension Lorentz groups that the set of possibilities is very irregular, but because everything is finite it feels like a complete list could be enumerated, perhaps by computer, but I can't find anything even approaching it.

*I know that in lower dimensions there are more possibilities for supersymmetry because of anyons and similar phenomena. I wouldn't be surprised if below a certain dimension it becomes infinitely more complicated, but I don't know if and where that happens.

asked Aug 13, 2015 in Theoretical Physics by Exomnium (20 points) [ revision history ]
edited Aug 13, 2015 by Exomnium

1 Answer

+ 2 like - 0 dislike

Those "central" extensios are classified in

(I understand that this does not answer your entire question, but it seems to answer the first part.)

answered Sep 14, 2017 by Urs Schreiber (6,095 points) [ revision history ]

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