Supertwistor formulation for massless superparticle in AdS5 × S5 superspace

Abstract

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

Multitwistor mechanics of massless superparticle on AdS5 × S5 superbackground

“…Using the defining conditions for the spinor (Lorentz) harmonics we show that it is possible to exclude half of them from the expressions for the momentum components tangent to AdS 5 and S 5 parts of the background. Reduced expressions for the momentum components coincide with those proposed in [48] and allow to obtain four-supertwistor formulation of the superparticle. Since these supertwistors precisely coincide with those found in [22], we actually find the relation between the eight-and four-supertwistor formulations of the massless superparticle on AdS 5 × S 5 superbackground.…”

“…Dotted and undotted letters from the beginning of the Latin alphabet label fundamental representation indices of the two SU(2) subgroups of Spin(1, 4) R . Details of the spinor algebra in D = 1 + 4 dimensions are given in [48] and Appendix A of the present paper. In particular, for n (0)…”

“…However, it is unclear how the incidence relations that connect supertwistor components and the superspace coordinates can be derived within this approach. This motivated us [48] to examine traditional root of introducing supertwistors starting with the first-order representation of the massless superparticle' Lagrangian on AdS 5 × S 5 superbackground. Then we expressed momentum components tangent to AdS 5 and S 5 parts of the background in terms of the SU(2)-Majorana spinors for Spin (1,4) and Spin (5) groups so that the 10-momentum null condition was translated into the constraint on the sum of the products of these spinors.…”

“…We identify the set of the constraints for supertwistors and calculate their classical superalgebra to show that, similarly to the bosonic particle case, there are present the second-class constraints. Then in section 5 it is considered reduced four-supertwistor formulation of the superparticle's Lagrangian proposed in [48] that is characterized only by the first-class constraints. We identify the set of equations for the quantized superparticle's wave function in the superambitwistor space.…”

Cubic interactions for arbitrary spin $$ \mathcal{N} $$ -extended massless supermultiplets in 4d flat space

“…7. Twistor methods addressed, e.g., in Refs [69,70],. could also be helpful for studying interactions of massless supermultiplets in higher dimensions.…”