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arXiv · 2204.04899

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

Evgeny I. Buchbinder·Benjamin J. Stone
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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 $T_{m n}$. 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 $\langle Q Q T\rangle $, $\langle \bar{Q} Q V\rangle $ and $\langle \bar{Q} Q T\rangle $ are not consistent with $\mathcal{N}=1$ supersymmetry

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Evgeny I. Buchbinder, Benjamin J. Stone. 2022-04-11. Three-point functions of fermionic higher-spin currents in 4D conformal field theory. https://doi.org/10.1103/physrevd.105.125004

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