N=1 Superconformal Symmetry in Four Dimensions

TL;DR

This paper analyzes the N=1 superconformal group in four dimensions, classifies its representations, and derives the general forms of two- and three-point correlation functions for superfields, highlighting the structure of supercurrents.

Contribution

It provides a group-theoretical classification of superconformal representations and explicit forms of correlation functions for supercurrents in four-dimensional N=1 theories.

Findings

Two-point supercurrent correlation function is unique up to a constant.

Three-point supercurrent correlation function has two free parameters.

Superfields are shown to be quasi-primary under superconformal transformations.

Abstract

N=1, d=4 superconformal group is studied and its representations are discussed. Under superconformal transformations, left invariant derivatives and some class of superfields, including supercurrents, are shown to follow these representations. In other words, these superfields are quasi-primary by analogy with two dimensional conformal field theory. Based on these results, we find the general forms of the two-point and the three-point correlation functions of the quasi-primary superfields in a group theoretical way. In particular, we show that the two-point function of the supercurrent is unique up to a constant and the general form of the three-point function of the supercurrent has two free parameters.