D=11 superstring model with 30 kappa--symmetries and 30/ 32 BPS states in an extended superspace

Abstract

A superstring model in the D=11 superspace maximally extended by antisymmetric tensor bosonic coordinates, $\\Sigma^{(528|32)}$, is proposed. It possesses 30 kappa-symmetries and 32 target space supersymmetries. The usual preserved supersymmetry--kappa-symmetry correspondence suggests that it describes the excitations of a BPS state preserving all but two supersymmetries. The model can also be formulated in any $\\Sigma^{({n(n+1)\\over 2}|n)}$ superspace, n=32 corresponding to D=11. It may also be treated as a `higher--spin generalization' of the usual Green--Schwarz superstring. Although the global symmetry of the model is a generalization of the super--Poincar\\'e group, ${\\Sigma}^{({n(n+1)\\over 2}|n)}\\times\\supsetSp(n)$, it may be formulated in terms of constrained OSp(2n|1) orthosymplectic supertwistors. We workout this supertwistor realization and its Hamiltonian dynamics. We also give the super--p--brane generalization of the model. In particular, the $\\Sigma^{(528|32)}$ supermembrane model describes excitations of a 30/ 32 BPS state, as the $\\Sigma^{(528|32)}$ superstring does, while the super--3--brane and the super--5--brane correspond, respectively, to 28/32 and 24/32 BPS states.