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

Abstract

We investigate the properties of a four-dimensional conformal field theory possessing a fermionic higher-spin current $Q_{\alpha (2k)\dot{\alpha }}$. 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 $V_m$, and with the energy-momentum tensor $T_{mn}$. In particular, the $k=1$ case corresponds to a "supersymmetry-like" current, that is, a fermionic conserved current with identical properties to the supersymmetry current which appears in $\mathcal{N}=1$ superconformal field theories. However, we show that in general, the three-point correlation functions $⟨QQT⟩$, $⟨\bar{Q}QV⟩$ and $⟨\bar{Q}QT⟩$ are not consistent with $\mathcal{N}=1$ supersymmetry

arXiv comment44 pages; v2: minor corrections

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