Higher Spin Conformal Symmetry for Matter Fields in 2+1 Dimensions

Abstract

A simple realization of the conformal higher spin symmetry on the free $3d$ massless matter fields is given in terms of an auxiliary Fock module both in the flat and $Ad{S}_3$ case. The duality between non-unitary field-theoretical representations of the conformal algebra and the unitary (singleton--type) representations of the $3d$ conformal algebra $sp(4,\mathbb{R})$ is formulated explicitly in terms of a certain Bogolyubov transform.

Minor corrections: report number is changed