OSp supergroup manifolds, superparticles and supertwistors

TL;DR

The work addresses constructing simple, twistor-like actions for superparticles propagating on AdS-related superspaces and supergroups, using Cartan forms that can be made quadratic in fermions. The main approach is to exploit coset and supergroup parametrizations of $OSp(1|4)/SO(1,3)$, $OSp(1|4)$, and $OSp(1|2n)$ to build actions that are linear in bosonic coordinates through bilinear spinor contractions, and quadratic in fermions, with contractions leading to several contractions that yield massless superparticles in Minkowski space and, optionally, tensorial central charges. Key contributions include explicit constructions of twistor-like actions on these superspaces, the identification of the Cartan forms that become quadratic in Grassmann coordinates, and the discovery of unusual κ-symmetry structures (notably three κ-symmetries for OSp(1|4) and (2n−1) for OSp(1|2n)). The findings have potential implications for simplifying brane actions in AdS backgrounds, and for connections to higher-spin field theories and branes in AdS superbackgrounds, with possible relevance to M-theory incarnations via OSp(1|32) and OSp(1|64).

Abstract

We construct simple twistor-like actions describing superparticles propagating on a coset superspace OSp(1|4)/SO(1,3) (containing the D=4 anti-de-Sitter space as a bosonic subspace), on a supergroup manifold OSp(1|4) and, generically, on OSp(1|2n). Making two different contractions of the superparticle model on the OSp(1|4) supermanifold we get massless superparticles in Minkowski superspace without and with tensorial central charges. Using a suitable parametrization of OSp(1|2n) we obtain even Sp(2n)-valued Cartan forms which are quadratic in Grassmann coordinates of OSp(1|2n). This result may simplify the structure of brane actions in super-AdS backgrounds. For instance, the twistor-like actions constructed with the use of the even 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.