Supermultiplet of $\beta-$deformations from twistors

TL;DR

This paper analyzes the supermultiplet of beta-deformations in N=4 SYM, comparing field theory and gravity descriptions, and introduces a twistor-based approach for studying related representations in AdS/CFT.

Contribution

It presents a new twistor-based method to study finite-dimensional representations of the superconformal algebra related to beta-deformations.

Findings

Supermultiplet structures are compared between field theory and gravity.

An intertwining operator relates two representations of the superconformal algebra.

A twistor approach is developed for analyzing nonunitary representations.

Abstract

We consider the supermultiplet of linearized beta-deformation of $\mathcal{N}=4$ Super Yang-Mills(SYM). It was previously studied on the gravitational side. We study the supermultiplet of beta-deformations on the field theory side and we compare two finite-dimensional representations of $psl(4|4,\bf{R})$ algebra. We show that they are related by an intertwining operator. We develop a twistor-based approach which could be useful for studying other finite-dimensional and nonunitary representations in AdS/CFT correspondence.