Operator product expansions in four-dimensional superconformal field theories

TL;DR

This paper explores the structure of operator product expansions in four-dimensional superconformal field theories, highlighting simplifications for certain operators and discussing how their Green's functions can be determined.

Contribution

It provides a detailed analysis of the OPE structure in 4D superconformal theories, emphasizing cases with simplified forms for chiral and analytic operators across different N supersymmetries.

Findings

OPE simplifies for chiral operators in N=1 and N=2

OPE simplifies for analytic operators in N=2 and N=4

Green's functions can be determined up to constants for these operators

Abstract

The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in $N=1$ and $N=2$, and for analytic operators, in $N=2$ and $N=4$. It is argued that the Green's functions of such operators can be determined up to constants.