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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.15407 |
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Table of Contents:
- We consider mixed four-point correlators of 1/2-BPS operators $\mathcal{O}_{k}$ in the maximally supersymmetric CFTs, i.e. the 3d $\mathcal{N}=8$, 4d $\mathcal{N}=4$, and 6d $\mathcal{N}=(2,0)$ theories. In arXiv:hep-th/0405180, Dolan, Gallot, and Sokatchev demonstrated that four-point correlators of identical $\mathcal{O}_{k}$ in these SCFTs can be expressed in terms of a number of unconstrained one- and two-variable ``reduced correlator" functions acted on by a $2(\varepsilon-1)$nd order differential operator $Δ_\varepsilon$, which is non-local in odd dimensions $d=2(\varepsilon+1)$. We generalize this construction to mixed correlators $\langle \mathcal{O}_{k_1}\mathcal{O}_{k_2}\mathcal{O}_{k_3}\mathcal{O}_{k_1+k_2+k_3-2\mathcal{E}}\rangle$ up to extremality $\mathcal{E}=2$. To construct superconformal blocks, we generalize the R-symmetry channel equations and use Jack polynomial expansions to recursively generate the full spectrum of conformal blocks in a superblock from a single channel. We observe that for each $\varepsilon$, this channel equation can be inverted to expand the reduced correlators in ``reduced superblocks" involving blocks with shifted external kinematics. These reduced blocks reproduce what is known in 4d, generalize the known $\langle \mathcal{O}_{2}\mathcal{O}_{2}\mathcal{O}_{k}\mathcal{O}_{k}\rangle$ case in 6d, and offer a novel result in 3d.