On the Unitarity of D=9,10,11 Conformal Supersymmetry

Recently, applications in string theory require the knowledge of the UIRs of the conformal superalgebras for D > 6. In these applications most prominent role play the superalgebras osp(1| 2n), cf., e.g., [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Initially, the superalgebra osp(1| 32) was put forward for D = 10 [1]. Later it was realized that osp(1| 2n) would fit any dimension, though they are minimal only forD = 3, 9, 10, 11 (for n = 2, 16, 16, 32, resp.) [7]. In all cases one needs to find first the UIRs of osp(1| 2n, IR). This was done for general n in [11]. In the present paper we consider the implications for conformal supersymmetry for D = 9, 10, 11.