Reduced superblocks at next-to-next-to-extremality for all half-maximally supersymmetric CFTs

TL;DR

This paper introduces simplified reduced correlator functions for mixed four-point correlators in various half-maximally supersymmetric conformal field theories, revealing new structural insights and generalizations across dimensions.

Contribution

It demonstrates that dynamical data in extremal correlators can be captured by reduced correlator functions with a block expansion, extending previous results to multiple dimensions.

Findings

Reduced correlator functions encode dynamical data in extremal correlators.

The reduced blocks involve ordinary blocks with shifted kinematics.

New results are obtained for 3d and 5d theories, generalizing known 6d cases.

Abstract

We consider mixed four-point correlators of 1/2-BPS operators $\phi_{k}$ in SCFTs with eight real Poincar\'e supercharges, namely the 3d $\mathcal{N}=4$, 4d $\mathcal{N}=2$, 5d $\mathcal{N}=1$, and 6d $\mathcal{N}=(1,0)$ theories. Using the basis of solutions to the superconformal Ward identity introduced in arXiv:hep-th/0405180, we demonstrate that the dynamical data in mixed correlators of extremality $\mathcal{E}=2$ is encoded in certain simpler ``reduced correlator" functions that admit a block expansion, in close analogy to the recent result for maximally supersymmetric CFTs in arXiv:2601.15407. These reduced blocks similarly involve ordinary blocks with shifted kinematics and reproduce what is known in 4d, generalize a known example in 6d, and offer novel results in 3d and 5d.