Mixed OPEs in ${\mathcal N}=2$ Superconformal Theories

TL;DR

This paper uses superspace methods to analyze the operator product expansion in ${ m N}=2$ superconformal theories, identifying possible operators in mixed correlators, advancing superconformal block analysis.

Contribution

It provides the first detailed computation of mixed OPEs involving stress-tensor, chiral, and flavor current multiplets in ${ m N}=2$ theories, solving symmetry and conservation constraints.

Findings

Identified all operators in the mixed OPEs consistent with ${ m N}=2$ superconformal symmetry.

Derived constraints on three-point functions involving different multiplets.

Laid groundwork for superconformal block analysis of mixed correlators.

Abstract

Using superspace techniques, we compute the mixed OPE between an ${\mathcal N}=2$ stress-tensor multiplet, a chiral multiplet and a flavor current multiplet. We perform a detailed analysis of the three-point function between two of the mentioned multiplets and a third arbitrary operator. We then solve all the constraints coming from the ${\mathcal N}=2$ superconformal symmetry and from the equations of motion and/or conservation equations, and obtain all the possible operators that can appear in the expansion. This calculation is the first step towards a more general superconformal block analysis of mixed correlators in ${\mathcal N}=2$ theories.