On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories

TL;DR

This work develops a dedicated harmonic superspace for 3d ${ m N}=6$ SCFTs to study BPS operator correlators, deriving comprehensive two- and three-point structures and constraining four-point functions via superconformal Ward identities. By exploiting a graded decomposition of ${ m osp}(6|4)$ and a coset construction, the authors obtain explicit covariants, invariants, and cross-ratios that organize correlators of ${ frac{1}{2}}$- and ${ frac{1}{3}}$-BPS multiplets. A key finding is that four-point functions of alternating chiralities admit Ward identities whose analysis reveals a solvable subsector that is topological, interpretable via cohomological reduction with a nilpotent supercharge ${f Q}$. The framework sets the stage for a 3d ${ m N}=6$ superconformal bootstrap, including potential connections to localization, integrability, and AdS$_4 imes ext{CP}^3$ holography, and provides tools to understand monopole operators within a constrained analytic structure.

Abstract

We introduce a novel harmonic superspace for $3d$ $\mathcal{N}=6$ superconformal field theories that is tailor made for the study of correlation functions of BPS operators. We calculate a host of two- and three-point functions in full generality and put strong constraints on the form of four-point functions of some selected BPS multiplets. For the four-point function of $\frac{1}{2}$-BPS operators we obtain the associated Ward identities by imposing the absence of harmonic singularities. The latter imply the existence of a solvable subsector in which the correlator becomes topological. This mechanism can be explained by cohomological reduction with respect to a special nilpotent supercharge.