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arXiv · 2607.10133

Superspace invariants and 3-point correlators in 3d $\mathcal{N}=3,4$ SCFTs

Aditya Jain·Amin A. Nizami
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Abstract

We use the auxiliary polarization spinor formalism together with superspace techniques to construct a complete and minimal list of 3-point invariant structures in three-dimensional superconformal field theories (SCFTs) with $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal symmetry. The existence of non-abelian $R$-symmetry for $\mathcal{N}=3,4$ gives rise to novel invariant structures built from the antisymmetric invariant tensor. These invariants are used to enumerate the structural form of spinning 3-point correlators of general as well as conserved spinning superfield operators in 3d SCFTs. For conserved operators, we find that the $\mathcal{N}=3$ correlators are fixed upto one parity-even and one parity-odd structure, while $\mathcal{N}=4$ conserved correlators admit two parity-even structures and one parity-odd structure, with the second parity-even structure associated with mirror symmetry breaking.

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Aditya Jain, Amin A. Nizami. 2026-07-11. Superspace invariants and 3-point correlators in 3d $\mathcal{N}=3,4$ SCFTs. https://arxiv.org/abs/2607.10133

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