OSp supergroup manifolds, superparticles, and supertwistors

Abstract

We construct simple twistor-like actions describing superparticles propagating on a coset superspace $\mathrm{OSp}(1|4)/\mathrm{SO}(1,3)$ (containing the $D=4$ anti--de Sitter space as a bosonic subspace), on a supergroup manifold $\mathrm{OSp}(1|4)$ and, generically, on $\mathrm{OSp}(1|2n).$ Making two different contractions of the superparticle model on the $\mathrm{OSp}(1|4)$ supermanifold we get massless superparticles in Minkowski superspace without and with tensorial central charges. Using a suitable parametrization of $\mathrm{OSp}(1|2n)$ we obtain even $\mathrm{Sp}(2n)$-valued Cartan forms which are quadratic in Grassmann coordinates of $\mathrm{OSp}(1|2n).$ This result may simplify the structure of brane actions in super--anti--de Sitter (AdS) backgrounds. For instance, the twistor-like actions constructed with the use of the even $\mathrm{OSp}(1|2n)$ Cartan forms as supervielbeins are quadratic in fermionic variables. We also show that the free bosonic twistor particle action describes massless particles propagating in arbitrary space-times with a conformally flat metric, in particular, in Minkowski space and AdS space. Applications of these results to the theory of higher spin fields and to superbranes in AdS superbackgrounds are mentioned.