Supertwistor formulation for massless superparticle in AdS5 × S5 superspace

Abstract

Starting with the first-order formulation of the massless superparticle model on the AdS5×S5 superbackground and presenting the momentum components tangent to AdS5 and S5 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)⊕u(1) gauge algebra. This justifies previously proposed group-theoretic definition of the AdS5×S5 supertwistors and allows to derive the incidence relations with the (10|32) supercoordinates of the AdS5×S5 superspace. Whenever superparticle moves within the AdS5 subspace of the AdS5×S5 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)⊕u(1) generators single out upon quantization the states of D=5 N=8 gauged supergravity multiplet in the superambitwistor formulation.