OSp supergroup manifolds, superparticles and supertwistors

TL;DR

This paper develops twistor-like actions for superparticles on various supermanifolds, simplifying the structure of brane actions in super-AdS backgrounds and exploring applications to higher spin fields and superbranes.

Contribution

It introduces new twistor-like actions for superparticles on OSp supermanifolds, including contractions to Minkowski space, and presents quadratic fermionic structures that may simplify superbrane theories.

Findings

Constructed twistor-like actions on OSp(1|4)/SO(1,3) and OSp(1|2n) supermanifolds.

Derived massless superparticles in Minkowski space via contractions.

Presented quadratic fermionic forms for supervielbeins in super-AdS backgrounds.

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.