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arXiv · 2108.01865

Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory

Evgeny I. Buchbinder·Benjamin J. Stone
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Abstract

We consider $\mathcal{N=1}$ superconformal field theories in three-dimensions possessing a conserved current multiplet $\mathcal{F}_{ (α_{1} α_{2} α_{3} α_{4}) }$ which we refer to as the superspin-2 current multiplet. At the component level it contains a conserved spin-2 current different from the energy-momentum tensor and a conserved fermionic higher spin current of spin 5/2. Using a superspace formulation, we calculate correlation functions involving $\mathcal{F}$, focusing particularly on the three-point function $ \langle \mathcal{F} \mathcal{F} \mathcal{F} \rangle $. After imposing the constraints arising from conservation equations and invariance under permutation of superspace points, we find that the parity-even and parity-odd sectors of this three-point function are each fixed up to a single coefficient. The presence of the parity-odd contribution is rather non-trivial, as there is an apparent tension between supersymmetry and the existence of parity-odd structures.

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Evgeny I. Buchbinder, Benjamin J. Stone. 2021-11-15. Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory. https://doi.org/10.1103/physrevd.104.106004

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