Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and $osp(L,2M)$ Invariant Equations in Generalized (Super)Space

TL;DR

This paper explores conformal higher spin symmetries in 4d supermultiplets, extending to generalized superspaces with $osp(L,2M)$ invariance, and discusses dualities and representations relevant to higher spin theories.

Contribution

It provides a detailed realization of conformal higher spin symmetries on 4d supermultiplets, including duality relations and extensions to generalized superspaces with $osp(L,2M)$ invariance.

Findings

Supermultiplets form representations of $sp(8)$.

Duality between non-unitary and unitary representations is formulated.

Higher spin equations are extended to $osp(L,2M)$ invariant superspaces.

Abstract

Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized ${\cal N}=4$ SYM theory, are considered in some detail. Duality between non-unitary field-theoretical representations and the unitary doubleton--type representations of the 4d conformal algebra $su(2,2)$ is formulated in terms of a Bogolyubov transform. The set of 4d massless fields of all spins is shown to form a representation of $sp(8)$. The obtained results are extended to the generalized superspace invariant under $osp(L, 2M)$ supersymmetries. World line particle interpretation of the free higher spin theories in the $osp(2\N, 2M)$ invariant (super)space is given. Compatible with unitarity free equations of motion in the $osp(L,2M)$ invariant (super)space are formulated. A conjecture on the chain of $AdS_{d+1}/CFT_d \to AdS_{d}/CFT_{d-1} \to ...$ dualities in the higher spin gauge theories is proposed.