Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins

TL;DR

This paper introduces a new constructive method for solving conservation conditions in three-point conformal correlation functions involving higher spins, linking them to algebraic tensor constructions and AdS/CFT duality.

Contribution

The authors propose a novel approach to construct higher-spin conformal correlation functions using tensor combinations, verified for spins three and four, and connect these to AdS space interactions.

Findings

Verified the tensor construction hypothesis for spins three and four.

Reduced the problem to algebraic cancellation of divergence terms.

Linked solutions to AdS space cubic interactions.

Abstract

We propose a new constructive approach to the solutions of the conservation condition for the three-point conformal correlation function in the Osborn-Petkou formulation generalized by the authors for higher spins. We propose for correlation functions of the same spin conformal currents the general hypothesis that the Osborn-Petkou structural tensor of higher spins satisfying the right symmetry conditions can be obtained from the combination of the principal terms of spin one and two structural tensors raised to the degree corresponding to the value of spin s. We verified this hypothesis for the case of spin three and four and showed that the construction of the conserved three-point function can be reduced to the algebraic task of canceling the right hand sides of the divergences of constructed terms. Moreover it follows from this consideration that for spin three and four cases our solutions can be interpreted as the $CFT$-dual to the cubic interaction in the AdS space with one dimension more.