On The Construction And The Structure Of Off-Shell Supermultiplet Quotients

Recent efforts to classify representations of supersymmetry with no central charge [C. F. Doran et al., Adv. Theor. Math. Phys. 15, 1909 (2011)] have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle in the paper by Doran et al., Int. J. Mod. Phys. A 22, 869 (2007): such (gauge-)quotients are not Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl\u27s construction that is known to produce all finite-dimensional unitary representations in Lie algebras. © 2012 World Scientific Publishing Company