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

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.

Fixed typos in Eq (3.11), (3.13), (3.14), (3.20) and (3.30)