Supertwistor formulation for massless superparticle in $AdS_5\times S^5$ superspace

TL;DR

This paper develops a supertwistor formulation for the massless superparticle in $AdS_5\times S^5$ superspace, enabling a quadratic Lagrangian and linking supertwistors to superspace coordinates, with implications for supergravity state quantization.

Contribution

It introduces a supertwistor-based Lagrangian for the superparticle in $AdS_5\times S^5$, deriving incidence relations and gauge constraints, and connects supertwistor variables to superspace coordinates.

Findings

Superparticle's Lagrangian expressed quadratically in supertwistors.

Derived incidence relations with superspace coordinates.

Quantization yields states of $D=5$ $N=8$ gauged supergravity.

Abstract

Starting with the first-order formulation of the massless superparticle model on the $AdS_5\times S^5$ superbackground and presenting the momentum components tangent to $AdS_5$ 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 $AdS_5\times S^5$ supertwistors and allows to derive the incidence relations with the $(10|32)$ supercoordinates of the $AdS_5\times S^5$ superspace. Whenever superparticle moves within the $AdS_5$ subspace of the $AdS_5\times S^5$ 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.