Short representations of SU(2, 2/N) and harmonic superspace analyticity

We consider the harmonic superspaces associated to SU(2, 2/N) superconformal algebras. For arbitrary N , we show that massless representations, other than the chiral ones, correspond to [N2 ] “elementary” ultrashort analytic superfields whose first component is a scalar in the k antisymmetric irrep of SU(N) (k = 1 . . . [N2 ]) with top spin Jtop = ( N 2 − k 2 , 0 ) . For N = 2n we analyze UIR’s obtained by tensoring the self-conjugate ultrashort multiplet Jtop = ( n 2 , 0 ) and show that N−1 different basic products give rise to all possible UIR’s with residual shortening. UMR 5108 associée à l’Université de Savoie