Three-point functions of a fermionic higher-spin current in 4D conformal field theory

We investigate the properties of a four-dimensional conformal field theory possessing a fermionic higher-spin current Qα(2k)α˙. Using a computational approach, we examine the number of independent tensor structures contained in the three-point correlation functions of two fermionic higher-spin currents with the conserved vector current Vm and with the energy-momentum tensor Tmn. In particular, the k=1 case corresponds to a "supersymmetrylike"current, that is, a fermionic conserved current with identical properties to the supersymmetry current which appears in N=1 superconformal field theories. However, we show that in general, the three-point correlation functions QQV and QQT are not consistent with N=1 supersymmetry.