Operator algebra of free conformal currents via twistors

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 $Ad{S}_4/CF{T}_3$ framework. Generating function for $n$-point functions of 4d conformal currents is also presented.

51 pages, V2: typos and coefficients corrected; acknowledgement, clarifications and a new section on the derivation of butterfly formulae for current OPE from multiparticle algebra are added. Derivation of space-time current operator algebra is simplified. V3: Discussion of independent three-point functions for 4d conserved currents of different spins is added in Section 9.2

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