Operator algebra of free conformal currents via twistors

TL;DR

This work derives the operator algebra of free conformal higher-spin currents in generalized matrix spaces ${\cal M}_M$ using unfolded dynamics in twistor space. By identifying the algebra of currents with the multiparticle algebra ${\mathbf M}$ and organizing multi-current products via butterfly algebras, the authors obtain compact determinant-type generating functions that encode all $n$-point functions for both 3d and 4d conformal currents. The construction reproduces known 2- and 3-point results, extends to supercurrents, and reveals a deep HS symmetry structure that unifies boundary and bulk (AdS) descriptions. The approach provides a principled route to compute correlators and suggests a path toward a multiparticle HS/string-like framework with potential deformations and holographic extensions.

Abstract

Operator algebra of (not necessarily free) higher-spin conformal conserved currents in generalized matrix spaces, that include 3d Minkowski space-time as a particular case, is shown to be determined by an associative algebra $M$ of functions on the twistor space. For free conserved currents, $M$ is the universal enveloping algebra of the higher-spin algebra. Proposed construction greatly simplifies computation and analysis of correlators of conserved currents. Generating function for $n$-point functions of 3d (super)currents of all spins, built from $N$ free constituent massless scalars and spinors, is obtained in a concise form of certain determinant. Our results agree with and extend earlier bulk computations in the HS $AdS_4/CFT_3$ framework. Generating function for $n$-point functions of 4d conformal currents is also presented.