Operator algebra of free conformal currents via twistors

TL;DR

This paper develops an algebraic framework using twistors to analyze operator algebras of higher-spin conformal currents, simplifying correlator computations and extending previous results in AdS/CFT correspondence.

Contribution

It introduces an associative algebra approach based on twistors for higher-spin currents, providing a unified method to compute correlators in various dimensions.

Findings

Derived operator algebra from twistor functions for higher-spin currents.

Obtained concise generating functions for n-point correlators in 3d and 4d.

Extended earlier bulk computations in the HS AdS4/CFT3 framework.

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.