Superconformal invariants and spinning correlators in 3d $\cal{N}=2$ SCFTs

TL;DR

This paper develops superconformal invariants in superspace to systematically construct and analyze 3-point correlators of spinning operators in 3d $\

Contribution

It introduces a minimal set of invariants for 3d $\

Findings

Explicit construction of superconformal invariants for 3d $\

Evidence that conserved current correlators have parity-even and parity-odd parts

Abstract

We construct superconformal invariants in superspace which are used to build 3-point correlators of spinning operators in general $\cal{N}=2$ superconformal field theories in three dimensions. Our systematic analysis includes various relations between these invariants and provides a minimal set of parity-even and parity-odd invariants which is further used to construct general 3-point functions in any 3d $\cal{N}=2$ SCFT. For conserved (super)currents, we explicitly compute various 3-point functions using Wick contractions in the free field case, and express them in terms of the constructed parity-even invariants. We give evidence through examples for the claim that the 3-point function of conserved currents generally comprises of two parts - a parity-even piece coming from the free theory, and a parity-odd piece.