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

TL;DR

This paper develops a new harmonic superspace framework for 3d N=6 superconformal theories, enabling detailed analysis of BPS operator correlation functions and revealing a topological subsector through cohomological reduction.

Contribution

Introduces a novel harmonic superspace for 3d N=6 SCFTs, facilitating the calculation and constraint of BPS operator correlation functions.

Findings

Calculated two- and three-point functions in generality

Derived Ward identities for four-point functions of BPS operators

Identified a topological subsector via cohomological reduction

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.