Melik Karapetyan

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 [68] generalized by the authors [94] 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.

We revisit the problem of classification and explicit construction of the conformal three-point correlation functions of currents of arbitrary integer spin in arbitrary dimensions. For the conserved currents, we set up the equations for the conservation conditions and solve them completely for some values of spins, confirming the earlier counting of the number of independent structures matching them with the higher-spin cubic vertices in one higher dimension. The general solution for the correlators of conserved currents we delegate to a follow-up work.

Local quartic interaction of higher-spin gauge field with a scalar field is considered. In this special case, the nontrivial task of construction of interacting Lagrangian for the higher spin field in physical gauge was solved using the full power of Noether's procedure. As a result, the linear on-field gauge transformation is obtained and the corresponding commutator of transformation is analyzed. To understand the closure of this algebra the right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions with different higher spin symmetric tensor fields and with mixed symmetry tensor fields transformations.

We present the calculation of the solution of recurrence relations for radial pullback of cubic interaction in AdS_d + 1 by using Wolfram Mathematica as an effective tool for computing large expressions. Investigation of the results of these calculations allows us to guess the ansatz for solution and then obtain it completely.