Multitwistor mechanics of massless superparticle on $Ad{S}_5\times S^5$ superbackground

Abstract

Supertwistors relevant to $Ad{S}_5\times S^5$ superbackground of IIB supergravity are studied in the framework of the $D=10$ massless superparticle model in the first-order formulation. Product structure of the background suggests using $D=1+4$ Lorentz-harmonic variables to express momentum components tangent to $Ad{S}_5$ and $D=5$ harmonics to express momentum components tangent to $S^5$ that yields eight-supertwistor formulation of the superparticle's Lagrangian. We find incidence relations of the supertwistors with the $Ad{S}_5\times S^5$ superspace coordinates and the set of the quadratic constraints they satisfy. It is shown how using the constraints for the (Lorentz-)harmonic variables it is possible to reduce eight-supertwistor formulation to the four-supertwistor one. Respective supertwistors agree with those introduced previously in other models. Advantage of the four-supertwistor formulation is the presence only of the first-class constraints that facilitates analysis of the superparticle model.

25 pages. v2: presentation refined at the end of Sec.5, typos corrected. Version accepted for publication

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Cited by in corpus (3)

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• Oscillator approach to quantization of $Ad{S}_5\times S^5$ superparticle in twistor formulation