Supertwistor formulation for massless superparticle in $Ad{S}_5\times S^5$ superspace

Abstract

Starting with the first-order formulation of the massless superparticle model on the $Ad{S}_5\times S^5$ superbackground and presenting the momentum components tangent to $Ad{S}_5$ and $S^5$ subspaces as bilinear combinations of the constrained $SU(2)$-Majorana spinors allows to bring the superparticle's Lagrangian to the form quadratic in supertwistors. The $SU(2,2|4)$ supertwistors are assembled into a pair of $SU(2)$ doublets, one of which has even $SU(2,2)$ and odd $SU(4)$ components, while the other has odd $SU(2,2)$ and even $SU(4)$ components. They are subject to the first-class constraints that generate the $psu(2|2)\oplus u(1)$ gauge algebra. This justifies previously proposed group-theoretic definition of the $Ad{S}_5\times S^5$ supertwistors and allows to derive the incidence relations with the $(10|32)$ supercoordinates of the $Ad{S}_5\times S^5$ superspace. Whenever superparticle moves within the $Ad{S}_5$ subspace of the $Ad{S}_5\times S^5$ space-time, twistor formulation of its Lagrangian involves just one $SU(2)$ doublet of $SU(2,2|4)$ supertwistors with even $SU(2,2)$ and odd $SU(4)$ components. If in addition particle's 5-momentum is null, four first-class constraints which are the $su(2)\oplus u(1)$ generators single out upon quantization the states of $D=5$ $N=8$ gauged supergravity multiplet in the superambitwistor formulation.

24 pages, LaTeX; v4: in Sec.2.3 corrected wrong expressions for variations of supertwistors and Lagrange multipliers under gauge symmetries

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Cited by in corpus (9)

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• Cubic interactions for arbitrary spin N-extended massless supermultiplets in 4d flat space
• Cubic interactions of arbitrary spin fields in 3d flat space
• Supertwistor realisations of AdS superspaces
• Embedding formalism for $\mathcal{N}$-extended AdS superspace in four dimensions
• Multitwistor mechanics of massless superparticle on $Ad{S}_5\times S^5$ superbackground
• Embedding formalism for $(p,q)$ AdS superspaces in three dimensions
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• Oscillator approach to quantization of $Ad{S}_5\times S^5$ superparticle in twistor formulation