Three-point functions of conserved currents in 3D CFT: General formalism for arbitrary spins

Abstract

We analyse the general structure of the three-point functions of conserved higherspin supercurrents in 3D, N = 1 superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-

Three-point functions of conserved currents in 4D CFT: General formalism for arbitrary spins

“…Analogous to the approach of [75] we utilise auxiliary spinors to streamline the calculations. Consider a general spin-tensor…”

“…The study of their correlation functions is therefore of fundamental importance. The systematic approach to study correlation functions of conserved currents was developed in [11,12], and was later extended to superconformal field theories in various dimensions [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. 1 The most studied examples of conserved currents in (super)conformal field theory are the energy-momentum tensor and vector currents; their most general three-point functions were determined in [11,12].…”

“…In this paper we develop a general formalism to study the three-point correlation function of higher-spin supercurrent multiplets J α(i) α(j) corresponding to Lorentz type (i/2, j/2) with i, j ≥ 0. To undertake the analysis we augment the formalism developed by Park and Osborn [13,14,17] with auxiliary spinors, similar to the approach of [51] (see also [27,74,75]). The advantages of our approach are two-fold; first, by using the formalism of Park and Osborn the three-point function is completely determined by a constrained tensor H Ā1 Ā2 A 3 (X, Θ, Θ) which is a function of the superconformally covariant three-point building blocks X α α, Θ α , Θ α (the dependence on the superspace points is implicit).…”

“…In Subsection 3.1 we show how to classify the structures in the three-point function based on their transformation properties under superinversion. In Subsection 3.3 we introduce an index-free auxiliary spinor formalism based on [51] (see also [27,28,74,75]) to construct the supersymmetric three-point functions, and we outline the pertinent aspects of our computational approach. Next, in Section 4 we demonstrate our formalism by analysing the three-point functions involving the supercurrent and flavour current multiplets, where we reproduce the results previously found in [14,24,25,74].…”