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

Abstract

A supersymmetric string 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 ${\Sigma }^{(\frac{n(n+1)}{2}|n)}$ 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--Poincaré group, ${\Sigma }^{(\frac{n(n+1)}{2}|n)}\times \supset Sp(n)$, it may be formulated in terms of constrained OSp(2n|1) orthosymplectic supertwistors. We work out this supertwistor realization and its Hamiltonian dynamics. We also give the supersymmetric p-brane generalization of the model. In particular, the ${\Sigma }^{(528|32)}$ supersymmetric membrane model describes excitations of a 30/32 BPS state, as the ${\Sigma }^{(528|32)}$ supersymmetric string does, while the supersymmetric 3-brane and 5-brane correspond, respectively, to 28/32 and 24/32 BPS states.

arXiv comment23 pages, RevTex4. V2: minor corrections in title and terminology, some references and comments added

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