Supertwistor formulation for massless superparticle in \(AdS_{5} \times S^{5}\) superspace

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Abstract: Starting with the first-order formulation of the massless superparticle model on the

A d S_{5} i m e s S^{5}

superbackground and presenting the momentum components tangent to

A d S_{5}

and

S^{5}

subspaces as bilinear combinations of the constrained

S U (2)

-Majorana spinors allows to bring the superparticle's Lagrangian to the form quadratic in supertwistors. The

S U (2, 2 | 4)

supertwistors are assembled into a pair of

S U (2)

doublets, one of which has even

S U (2, 2)

and odd

S U (4)

components, while the other has odd

S U (2, 2)

and even

S U (4)

components. They are subject to the first-class constraints that generate the

p s u (2 | 2) o p l u s u (1)

gauge algebra. This justifies previously proposed group-theoretic definition of the

A d S_{5} i m e s S^{5}

supertwistors and allows to derive the incidence relations with the

(10 | 32)

supercoordinates of the

A d S_{5} i m e s S^{5}

superspace. Whenever superparticle moves within the

A d S_{5}

subspace of the

A d S_{5} i m e s S^{5}

space-time, twistor formulation of its Lagrangian involves just one

S U (2)

doublet of

S U (2, 2 | 4)

supertwistors with even

S U (2, 2)

and odd

S U (4)

components. If in addition particle's 5-momentum is null, four first-class constraints which are the

s u (2) o p l u s u (1)

generators single out upon quantization the states of

D = 5

N = 8

gauged supergravity multiplet in the superambitwistor formulation.

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